How to find the solution to an equation - ISEE Lower Level (grades 5-6) Mathematics Achievement

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Question

If Elaine is six years younger than twice Jack's age, and Jack is currently 12, how old is Elaine?

Answer

If Elaine is six years younger than twice Jack's age, and Jack is currently 12, how old is Elaine?

We must rewrite this word problem in terms of an equation.

The phrase 'six years younger than twice Jack's age' indicates the algebraic expression

2 x Jack's age – 6

If Jack is currently 12, we can simply plug in this value into our expression to get

2 x 12 – 6

Remember "order of operations"! Multiplication comes before subtraction.

24 – 6 =

Elaine is currently 18 years old.

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Question

Determine the value of $\dpi{100} x$ .

$\dpi{100} \small 3x+4=19$

Answer

Find which answer makes the equation true.

$\dpi{100} 3(5)+4=19$

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Question

Solve for $\dpi{100} t$ .

$\dpi{100} 7t-12=51$

Answer

$\dpi{100} 7(9)-12=51$

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Question

Simplify

$\dpi{100} 2x+10-5+6x$

Answer

Combine the $\dpi{100} 2x$ and the $\dpi{100} 6x$ to get $\dpi{100} 8x$

$\dpi{100} 10-5=5$

$\dpi{100} 8x+5$

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Question

Solve for :

Answer

First subtract 12 from both sides

Now divide both sides by 3.

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Question

Solve for :

Answer

First add to both sides

Now divide both sides by

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Question

Determine the value of

Answer

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Question

Determine the value of

Answer

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Question

Simplify

Answer

Combine like terms:

So

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Question

Solve for .

Answer

Replace the variable so the equation is correct.

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Question

Solve for .

Answer

Find the anwer for __which makes the equation true:

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Question

Evaluate the expression if .

$2x^{2}+4x-15$

Answer

$2x^{2}+4x-15$

To solve, insert 7 for each .

When solving this part of the equation, remember the order of operations (PEMDAS) and square the number in the parentheses BEFORE multiplying by 2.

$2(7)^{2}+4(7)-15$

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Question

Determine the value of .

$-2x^{2} +36 = -14$

Answer

To solve, we need to isolate .

$-2x^{2} +36 = -14$

Subtract $\small 36$ from both sides.

Divide both sides by $\small -2$ .

$\frac{-2x^2}{-2}=\frac{-50}{-2}$

Now, take the square root of both sides.

$\sqrt{x^2}=\sqrt{25}$

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Question

Simplify the expression.

$-7x^{^{2}}-2x +6x -3 +3x^{2}$

Answer

To simplify, you will need to combine like terms.

First, combine the two terms that have an $x^{2}$ .

$-7x^{2}+3x^{2}=-4x^{2}$

Then combine the two terms that have an .

Last, put them all together.

$-4x^{2} +4x -3$

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Question

What value of makes this statement true?

Answer

Subtract 12 from both sides:

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Question

What value of makes this statement true?

Answer

Add 12 to each side:

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Question

Which expression is equal to 15?

Answer

Keep in mind the order of operations for this problem. Always start with parentheses. There are no exponents here, so then move to multiplication and division, and finally to addition and subtraction.

$\left ( 4\times 8 \right )-5+3=30$

$4\times 8-\left ( 5+3 \right )=24$

$4\times \left ( 8-5+3 \right )=24$

$4\times \left ( 8-5 \right )+3=15$

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Question

What is a reasonable estimate of $\frac{73\times 943}{25}$ ?

Answer

Since multiplication and division have an equal status within the order of operations, we can start by dividing two of the elements (we don't have to multiply $73\times 943$ ). The first thing that should pop out is that $73\div 25$ equals a little less than .

Now we can estimate a reasonable range by multiplying by and . That would give us an approximate range of This estimate falls right in the middle of , which is the correct answer.

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Question

What is the value of

$20 \div 4 + 6 - 3^{2} + (2+2)^{2}-5\ ?$

Answer

Follow the order of operations for this problem:

parentheses: $20\div 4+6-3^{2}+4^{2}-5$

exponents: $20\div 4+6-9+16-5$

division and multiplication:

addition and subtraction: (now simply add and subtract from left to right!):

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Question

Solve when .

$2t^{2}-7t+4=$

Answer

$2(-3)^{2}-7(-3)+4=$

The solution is 43.

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