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ISEE Middle Level Math : Equations

Study concepts, example questions & explanations for ISEE Middle Level Math

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All ISEE Middle Level Math Resources

6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #21 : Equations

$\displaystyle 7(6+11+4)=$

Possible Answers:

$\displaystyle 28$

$\displaystyle 42$

127 $\displaystyle 127$

147 $\displaystyle 147$

Correct answer:

147 $\displaystyle 147$

Explanation:

First, add up the numbers in the parentheses:

$\displaystyle 7(6+11+4)=7(21)$

Then, multiply:

$\displaystyle 7(21)=147$

The answer is 147. $\displaystyle 147.$

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Example Question #21 : How To Find The Solution To An Equation

Sove for $\displaystyle x$ :

$\displaystyle 2x + 8 = 26$

Possible Answers:

x = 18 $\displaystyle x = 18$

x=34 $\displaystyle x=34$

x = 9 $\displaystyle x = 9$

x= 17 $\displaystyle x= 17$

x= 12 $\displaystyle x= 12$

Correct answer:

x = 9 $\displaystyle x = 9$

Explanation:

$\displaystyle 2x + 8 = 26$

$\displaystyle 2x + 8 -8= 26-8$

2x = 18 $\displaystyle 2x = 18$

$2x \div 2 = 18\div 2$ $\displaystyle 2x \div 2 = 18\div 2$

x = 9 $\displaystyle x = 9$

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Example Question #22 : Equations

Solve for $\displaystyle x$ :

$\displaystyle -3 (x + 9) = 36$

Possible Answers:

x=-15 $\displaystyle x=-15$

x=15 $\displaystyle x=15$

x= -21 $\displaystyle x= -21$

x=3 $\displaystyle x=3$

x=-3 $\displaystyle x=-3$

Correct answer:

x= -21 $\displaystyle x= -21$

Explanation:

$\displaystyle -3 (x + 9) = 36$

$-3 \cdot x +\left ( -3 \right ) \cdot 9 = 36$ $\displaystyle -3 \cdot x +\left ( -3 \right ) \cdot 9 = 36$

$\displaystyle -3 x -27= 36$

$\displaystyle -3 x -27+27 = 36+27$

$\displaystyle -3 x = 63$

$-3 x \div (-3)= 63\div (-3)$ $\displaystyle -3 x \div (-3)= 63\div (-3)$

x= -21 $\displaystyle x= -21$

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Example Question #23 : How To Find The Solution To An Equation

Solve for $\displaystyle x$ :

$\displaystyle 4x + 15 = x + 84$

Possible Answers:

$x= 24\frac{3}{4}$ $\displaystyle x= 24\frac{3}{4}$

x= 23 $\displaystyle x= 23$

$x = 17 \frac{1}{4}$ $\displaystyle x = 17 \frac{1}{4}$

$x = 13 \frac{4}{5}$ $\displaystyle x = 13 \frac{4}{5}$

x=33 $\displaystyle x=33$

Correct answer:

x= 23 $\displaystyle x= 23$

Explanation:

$\displaystyle 4x + 15 = x + 84$

$\displaystyle 4x -x + 15 = x -x + 84$

$\displaystyle 3x+ 15 = 84$

$\displaystyle 3x+ 15 -15= 84-15$

3x= 69 $\displaystyle 3x= 69$

$3x \div 3= 69\div 3$ $\displaystyle 3x \div 3= 69\div 3$

x= 23 $\displaystyle x= 23$

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Example Question #231 : Algebraic Concepts

Solve for $\displaystyle x$ :

$\displaystyle 5x - 15 = x + 84$

Possible Answers:

$x = 24\frac{3}{4}$ $\displaystyle x = 24\frac{3}{4}$

$x= 13\frac{4}{5}$ $\displaystyle x= 13\frac{4}{5}$

$x = 17\frac{1}{4}$ $\displaystyle x = 17\frac{1}{4}$

$x=16\frac{1}{2}$ $\displaystyle x=16\frac{1}{2}$

$x=11\frac{1}{2}$ $\displaystyle x=11\frac{1}{2}$

Correct answer:

$x = 24\frac{3}{4}$ $\displaystyle x = 24\frac{3}{4}$

Explanation:

$\displaystyle 5x - 15 = x + 84$

$\displaystyle 5x -x- 15 = x-x + 84$

$\displaystyle 4x- 15 = 84$

$\displaystyle 4x-15+ 15 = 84+15$

4x = 99 $\displaystyle 4x = 99$

$4x \div 4= 99\div 4$ $\displaystyle 4x \div 4= 99\div 4$

$x = 24\frac{3}{4}$ $\displaystyle x = 24\frac{3}{4}$

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Example Question #231 : Algebraic Concepts

Nathan is riding his bike to baseball practice. If he needs to travel 12 miles, how long will it take him to get there if he pedals at a rate of 5 miles per hour?

Possible Answers:

$2\ hours\ 24\ minutes$ $\displaystyle 2\ hours\ 24\ minutes$

$1\ hour$ $\displaystyle 1\ hour$

$4\ hours$ $\displaystyle 4\ hours$

$2\ hours$ $\displaystyle 2\ hours$

Correct answer:

$2\ hours\ 24\ minutes$ $\displaystyle 2\ hours\ 24\ minutes$

Explanation:

Divide:

$12\div 5=2.4$ $\displaystyle 12\div 5=2.4$

Answer: It will take Nathan at least 2 hours, plus an additional $0.4\times 60=24\ minutes$ $\displaystyle 0.4\times 60=24\ minutes$ .

So it will take him 2 hours and 24 minutes.

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Example Question #232 : Algebraic Concepts

3a+4=34 $\displaystyle 3a+4=34$

What is a?

Possible Answers:

$\displaystyle 4$

$\displaystyle 3$

$\displaystyle 10$

$\displaystyle 34$

$\displaystyle 30$

Correct answer:

$\displaystyle 10$

Explanation:

First, subtract:

$\displaystyle 3a+4-4=34-4$

3a=30 $\displaystyle 3a=30$

Then divide each side by 3:

$\frac{3a}{3}=\frac{30}{3}$ $\displaystyle \frac{3a}{3}=\frac{30}{3}$

a=10 $\displaystyle a=10$

Answer: 10

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Example Question #233 : Algebraic Concepts

9b+6=24 $\displaystyle 9b+6=24$

What is b?

Possible Answers:

$\displaystyle 30$

$\displaystyle 6$

$\displaystyle 2$

$\displaystyle 9$

$\displaystyle 18$

Correct answer:

$\displaystyle 2$

Explanation:

First, subtract 6 from each side:

$\displaystyle 9b+6-6=24-6$

9b=18 $\displaystyle 9b=18$

Then, divide each side by 9:

$\frac{9b}{9}=\frac{18}{9}$ $\displaystyle \frac{9b}{9}=\frac{18}{9}$

b=2 $\displaystyle b=2$

Answer: 2

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Example Question #234 : Algebraic Concepts

4b+7=55 $\displaystyle 4b+7=55$

What is b?

Possible Answers:

$\displaystyle 12$

$\displaystyle 6$

$\displaystyle 8$

$\displaystyle 7$

Correct answer:

$\displaystyle 12$

Explanation:

First, subtract 7 from each side:

$\displaystyle 4b+7-7=55-7$

4b=48 $\displaystyle 4b=48$

Then, divide each side by 4:

$\frac{4b}{4}=\frac{48}{4}$ $\displaystyle \frac{4b}{4}=\frac{48}{4}$

b=12 $\displaystyle b=12$

Answer: 12

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Example Question #235 : Algebraic Concepts

7x+6=48 $\displaystyle 7x+6=48$

What is $\displaystyle x$ ?

Possible Answers:

$\displaystyle 7$

$\displaystyle 8$

$\displaystyle 5$

$\displaystyle 6$

Correct answer:

$\displaystyle 6$

Explanation:

First subtract 6 from both sides:

$\displaystyle 7x+6-6=48-6$

The, divide by 7 on each side:

$\frac{7x}{7}=\frac{42}{7}$ $\displaystyle \frac{7x}{7}=\frac{42}{7}$

x=6 $\displaystyle x=6$

Answer: 6

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ISEE Middle Level Math : Equations

Study concepts, example questions & explanations for ISEE Middle Level Math

All ISEE Middle Level Math Resources

Example Questions

Example Question #21 : Equations

Example Question #21 : How To Find The Solution To An Equation

Example Question #22 : Equations

Example Question #23 : How To Find The Solution To An Equation

Example Question #231 : Algebraic Concepts

Example Question #231 : Algebraic Concepts

Example Question #232 : Algebraic Concepts

Example Question #233 : Algebraic Concepts

Example Question #234 : Algebraic Concepts

Example Question #235 : Algebraic Concepts

All ISEE Middle Level Math Resources

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