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ISEE Middle Level Math : Algebraic Concepts

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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 #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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Example Question #1145 : Concepts

$\displaystyle 16a-3=29$

Solve for $\displaystyle a.$

Possible Answers:

$\displaystyle 48$

$\displaystyle 3$

$\displaystyle 2$

$\displaystyle 16$

$\displaystyle 32$

Correct answer:

$\displaystyle 2$

Explanation:

First, add 3 on both sides:

$\displaystyle 16a-3+3=29+3$

Then, divide by 16 on both sides:

$\frac{16a}{16}=\frac{32}{16}$ $\displaystyle \frac{16a}{16}=\frac{32}{16}$

a=2 $\displaystyle a=2$

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Example Question #236 : Algebraic Concepts

Henry walked five miles on Tuesday and five miles on Wednesday. On Thursday, he walked 8 miles. How many miles did Henry walk all together?

Possible Answers:

$\displaystyle 18$

$\displaystyle 10$

$\displaystyle 13$

$\displaystyle 6$

Correct answer:

$\displaystyle 18$

Explanation:

Add up all of the miles that Henry walked:

$\displaystyle 5+5+8=18$

Answer: Henry walked 18 miles.

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Example Question #2354 : Isee Middle Level (Grades 7 8) Mathematics Achievement

9a+2=83 $\displaystyle 9a+2=83$

What is $\displaystyle a$?

Possible Answers:

$\displaystyle 8$

$\displaystyle 2$

$\displaystyle 81$

$\displaystyle 9$

Correct answer:

$\displaystyle 9$

Explanation:

First, subtract 2 from each side:

$\displaystyle 9a+2-2=83-2$

9a=81 $\displaystyle 9a=81$

Then, divide each side by 9:

$\frac{9a}9}=\frac{81}{9}$ $\displaystyle \frac{9a}9}=\frac{81}{9}$

a=9 $\displaystyle a=9$

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Example Question #2355 : Isee Middle Level (Grades 7 8) Mathematics Achievement

$\displaystyle 6b+14=50$

What is $\displaystyle b$?

Possible Answers:

$\displaystyle 36$

$\displaystyle 6$

$\displaystyle 14$

$\displaystyle 5$

Correct answer:

$\displaystyle 6$

Explanation:

First, subtract 14 from each side:

$\displaystyle 6b+14-14=50-14$

6b=36 $\displaystyle 6b=36$

Then, divide each side by 6:

$\frac{6b}{6}=\frac{36}{6}$ $\displaystyle \frac{6b}{6}=\frac{36}{6}$

b=6 $\displaystyle b=6$

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : Algebraic Concepts

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

All ISEE Middle Level Math Resources

Example Questions

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

Example Question #1145 : Concepts

Example Question #236 : Algebraic Concepts

Example Question #2354 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #2355 : Isee Middle Level (Grades 7 8) Mathematics Achievement

All ISEE Middle Level Math Resources

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