How to solve two-step equations - High School Math

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Question

Answer

This is a two-step equation. First you must add the decimals up to have a singular variable element

$\left ( 2.4+1.6\right )X=16$

Then divide both sides by 4:

$\frac{4X}{4}=\frac{16}{4}$

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Question

Solve for

Answer

The goal is to get alone on one side. Therefore you subtract from both sides to get . Then divide both sides by to get alone.

.

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Question

Solve the equation for . (Round to two decimal places).

$\small 1.22n+4=3.5$

Answer

$\small 1.22n+4=3.5$

Subtract from both sides of the equation, and simplify.

$\small 1.22n+4-4=3.5-4$

$\small \small 1.22n=-0.50$

Divide both sides by . Be careful of the negative sign.

$\small \frac{1.22n}{1.22}=-\frac{0.50}{1.22}$

$\small n=-0.41$

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Question

Josie buys worth of groceries. The sales tax is . If she pays with , how much change should she get?

Answer

The sales tax is $12.38\cdot 0.03875=0.479$

The total grocery bill is .

The change is .

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Question

$15=\frac{Y}{3}-9$

Answer

First add 9 to both sides:

$15+(9)=\frac{Y}{3}-9+(9)$

$24=\frac{Y}{3}$

Then multiply both sides by 3:

$24\left ( 3\right )=\frac{Y}{3}\left ( 3\right )$

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Question

Solve for .

Answer

To solve, we must perform the same operations to both sides of the equation.

Add 7 to both sides.

Divide both sides by 3.

$\frac{3n}{3}=\frac{19}{3}$

$n=\frac{19}{3}$

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Question

Solve for :

$\frac{12}{x} + 9 = 13$

Answer

This equation can be solved in three steps.

First, subtract from both sides of the equation to isolate the variable and its coefficient on the left side of the equation.

$\frac{12}{x} + 9 = 13$

$\rightarrow (\frac{12}{x} + 9) - 9 = (13) - 9$

$\rightarrow \frac{12}{x} = 4$

Now multiply both sides by since cannot be solved for while it is in the denominator.

$(\frac{12}{x}) \times x = (4) \times x$

$\rightarrow 12 = 4x$

Finally, divide both sides by to isolate and find the solution.

$\frac{(12)}{4} = \frac{(4x)}{4}$

$\rightarrow 3 = x$

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Question

Solve the equation for .

$\frac{4}{x}+3=9$

Answer

$\small \small \frac{4}{x}+3=9$

Subtract from both sides and simplify.

$\small \small \frac{4}{x}+3-3=9-3=6$

$\small \small \frac{4}{x}=6$

Multiply both sides by to remove it from the denominator.

$\small \small \frac{4}{x}(x)=6(x)$

$\small 4=6x$

Divide both sides by .

$\small \frac{4}{6}=\frac{6x}{6}$

Simplify the fraction.

$\small x=\frac{4}{6}=\frac{2}{3}$

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Question

Solve for $\small a$ .

$\frac{12}{a}-7=-1$

Answer

$\frac{12}{a}-7=-1$

Add 7 to both sides.

$\frac{12}{a}-7+7=-1+7$

$\frac{12}{a}=6$

Multiply both sides by $\small a$ .

$\frac{12}{a}(a)=6a$

Divide both sides by 6.

$\frac{12}{6}=\frac{6a}{6}$

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Question

Solve for $\small x$ .

$(2x\div4) +5 = 25$

Answer

$(2x\div4) +5 = 25$

We need to isolate $\small x$ . First, subtract $\small 5$ from both sides.

$(2x\div4) +5-5 = 25-5$

$(2x\div4) = 20$

Multiply both sides by $\small 4$ .

$2x\div4 4= 204$

Finally, divide both sides by $\small 2$ .

$\frac{2x}{2}=\frac{80}{2}$

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Question

Solve for the value of $\small a$ .

$\frac{a}{4}+3=12$

Answer

$\frac{a}{4}+3=12$

We need to work to isolate the variable using inverse functions.

Subtract $\small 3$ from both sides.
$\frac{a}{4}+3-3=12-3$

$\frac{a}{4}=9$

Multiply both sides by $\small 4$ .

$(4)\frac{a}{4}=(4)(9)$

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Question

$x=\frac{2}{3}*18$

Solve for .

Answer

$x=\frac{2}{3}18$

From here, you can either plug this into your calculator, or take the equation in pieces:

$x=\frac{218}{3}$

$x=\frac{36}{3}$

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Question

$\frac{2}{3}*(x+5)=12$

Solve for .

Answer

To solve $\frac{2}{3}(x+5)=12$ , first we need to get rid of the fraction. Dividing by a fraction is the same as multiplying by a reciprocal, so multiply both sides by $\frac{3}{2}$ .

$\frac{2}{3}(x+5)=12$

$\frac{3}{2}\frac{2}{3}(x+5)=12\frac{3}{2}$

$x+5=12\frac{3}{2}$

$x+5=\frac{12*3}{2}$

$x+5=\frac{36}{2}$

Subtract from both sides.

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Question

A glass jar is filled to the top with 100 blue marbles, 75 red marbles, and 25 yellow marbles. Each time a marbles is picked from the jar, it must be returned to the jar before another marble is picked again. What is the probability of picking a red marble?

Answer

First, find the total number of marbles in the glass jar: marbles in total.

It is given that there are 75 red marbles, thus: .

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Question

$\frac{2}{3}x=10$

Solve for .

Answer

To solve $\frac{2}{3}x=10$ , we need to get rid of the fraction. To do that, we multiply both sides by the reciprocal of that fraction.

$\frac{3}{2}\frac{2}{3}x=10\frac{3}{2}$

$x=10\frac{3}{2}$

From here, you can either plug that fraction into your calculator or solve in pieces.

$x=\frac{103}{2}$

$x=\frac{30}{2}$

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Question

$\frac{3}{4}x=118+2$

Solve for .

Answer

To solve for , we need to isolate our variable. That means that we want ONLY the on the left side of the equation.

First, combine our like terms on the right side.

$\frac{3}{4}x=118+2$

$\frac{3}{4}x=120$

Now divide both sides by $\frac{3}{4}$ . Remember, dividing by a fraction is the same as multiplying by the reciprocal, so we're going to multiply both sides by $\frac{4}{3}$ .

$\frac{3}{4}x\frac{4}{3}=120\frac{4}{3}$

Since $\frac{3}{4}\frac{4}{3}=\frac{12}{12}=1$ , we can ignore it.

$x=\frac{120}{1}\frac{4}{3}$

$x=\frac{480}{3}$

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Question

Solve for if

$7x^{2}=112$

Answer

To solve for we must get all of the numbers on the other side of the equation of .

When solving a simple two-step equation we must remove the numbers that are interacting with in this order: Addition/Subtraction, Multiplication/Division, Exponents.

To do this in a problem where is being multiplied by a number, we must divide both sides of the equation by the number.

In this case the number is so we divide each side of the equation by to make it look like this

$\frac{7x^{2}}{7}=\frac{112}{7}$

Our new problem will look like this

$x^{2}=16$

We then must solve the polynomial.

To solve an equation with we must take the square root of each side of the equation to get by itself.

Doing this makes our problem look like

$\sqrt{x^{2}}=\sqrt{16}$

Then we perform the square root to get the answer

$x=\pm4$

Remember that $-4^{2}$ can also equal so our answer will be both positive and negative.

The final answer is $x=\pm4$ .

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Question

Solve for if

Answer

When there are variables and numbers on each side of the equation, to solve we must mathematically move the variables onto one side and the numbers onto the other.

To do this we put all of the variables on the right side of the equal sign by subtracting from each side of the equation to have

When adding or subtracting variables you only add or subtract the numbers in front of the variables. If there is no number the number value is .

Perform the math.

Then to get all of the integers to the left side we will add to both sides of the equation to have

Perform the math.

The answer is .

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Question

Solve for if .

Answer

When there are variables and numbers on each side of the equation, to solve we must mathematically move the variables onto one side and the numbers onto the other.

To do this we put all of the variables on the right side of the equal sign by subtracting from the each side of the equation to have

When adding or subtracting variables you only add or subtract the numbers in front of the variables. If there is no number the number value is .

Perform the math

Then to get all of the integers to the left side we will add to each side of the equation to have

Perform the math

At this point we must divide each side of the equation by the number that is in front of to get by itself

$\frac{120}{4}=\frac{4x}{4}$

Perform the math to find the answer .

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Question

Solve for if

$4x^{2}=324$

Answer

To solve for we must get all of the numbers on the other side of the equation as .

When solving a simple two-step equation we must remove the numbers that are interacting with in this order: Addition/Subtraction, Multiplication/Division, Exponents.

To do this in a problem where is being multiplied by a number, we must divide both sides of the equation by the number.

In this case the number is so we divide each side of the equation by to make it look like this

$\frac{4x^{2}}{4}=\frac{324}{4}$

Our simplified equation becomes

$x^{2}=81$

To solve an equation with we must take the square root of each side of the equation to get by itself.

Doing this makes our problem look like $\sqrt{x^{2}}=\sqrt{81}$

Then we perform the square root to get the answer $x=\pm9$

Remember that $-9^{2}$ can also equal so our answer will be both positive and negative.

The final answer looks like $x=\pm9$ .

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