2.8.1: Review Exercises

Review Exercises

Use the Language of Algebra

Use Variables and Algebraic Symbols

In the following exercises, translate from algebra to English.

317.

$3\cdot 8$

318.

$12-x$

319.

$24÷6$

320.

$9+2a$

321.

$50\ge 47$

322.

$3y<15$

323.

$n+4=13$

324.

$32-k=7$

Identify Expressions and Equations

In the following exercises, determine if each is an expression or equation.

325.

$5+u=84$

326.

$36-6s$

327.

$4y-11$

328.

$10x=120$

Simplify Expressions with Exponents

In the following exercises, write in exponential form.

329.

$2\cdot 2\cdot 2$

330.

$a\cdot a\cdot a\cdot a\cdot a$

331.

$x\cdot x\cdot x\cdot x\cdot x\cdot x$

332.

$10\cdot 10\cdot 10$

In the following exercises, write in expanded form.

333.

$8^4$

334.

$3^6$

335.

$y^5$

336.

$n^4$

In the following exercises, simplify each expression.

337.

$3^4$

338.

${10}^6$

339.

$2^7$

340.

$4^3$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

341.

$10+2\cdot 5$

342.

$(10+2)\cdot 5$

343.

$(30+6)÷2$

344.

$30+6÷2$

345.

$7^2+5^2$

346.

${(7+5)}^2$

347.

$4+3(10-1)$

348.

$(4+3)(10-1)$

Evaluate, Simplify, and Translate Expressions

Evaluate an Expression

In the following exercises, evaluate the following expressions.

349.

$9x-5\text{when}x=7$

350.

$y^3\text{when}y=5$

351.

$3a-4b\text{when}a=10,b=1$

352.

$bh\text{when}b=7,h=8$

Identify Terms, Coefficients and Like Terms

In the following exercises, identify the terms in each expression.

353.

$12n^2+3n+1$

354.

$4x^3+11x+3$

In the following exercises, identify the coefficient of each term.

355.

$6y$

356.

$13x^2$

In the following exercises, identify the like terms.

357.

$5x^2,3,5y^2,3x,x,4$

358.

$8,8r^2,8r,3r,r^2,3s$

Simplify Expressions by Combining Like Terms

In the following exercises, simplify the following expressions by combining like terms.

359.

$15a+9a$

360.

$12y+3y+y$

361.

$4x+7x+3x$

362.

$6+5c+3$

363.

$8n+2+4n+9$

364.

$19p+5+4p-1+3p$

365.

$7y^2+2y+11+3y^2-8$

366.

$13x^2-x+6+5x^2+9x$

Translate English Phrases to Algebraic Expressions

In the following exercises, translate the following phrases into algebraic expressions.

367.

the difference of $x$ and $6$

368.

the sum of $10$ and twice $a$

369.

the product of $3n$ and $9$

370.

the quotient of $s$ and $4$

371.

$5$ times the sum of $y$ and $1$

372.

$10$ less than the product of $5$ and $z$

373.

Jack bought a sandwich and a coffee. The cost of the sandwich was $\text{\$3}$ more than the cost of the coffee. Call the cost of the coffee $c.$ Write an expression for the cost of the sandwich.

374.

The number of poetry books on Brianna’s bookshelf is $5$ less than twice the number of novels. Call the number of novels $n.$ Write an expression for the number of poetry books.

Solve Equations Using the Subtraction and Addition Properties of Equality

Determine Whether a Number is a Solution of an Equation

In the following exercises, determine whether each number is a solution to the equation.

375.

$y+16=40$

1. ⓐ$24$
2. ⓑ$56$

376.

$d-6=21$

1. ⓐ$15$
2. ⓑ$27$

377.

$4n+12=36$

1. ⓐ$6$
2. ⓑ$12$

378.

$20q-10=70$

1. ⓐ$3$
2. ⓑ$4$

379.

$15x-5=10x+45$

1. ⓐ$2$
2. ⓑ$10$

380.

$22p-6=18p+86$

1. ⓐ$4$
2. ⓑ$23$

Model the Subtraction Property of Equality

In the following exercises, write the equation modeled by the envelopes and counters and then solve the equation using the subtraction property of equality.

381.

382.

Solve Equations using the Subtraction Property of Equality

In the following exercises, solve each equation using the subtraction property of equality.

383.

$c+8=14$

384.

$v+8=150$

385.

$23=x+12$

386.

$376=n+265$

Solve Equations using the Addition Property of Equality

In the following exercises, solve each equation using the addition property of equality.

387.

$y-7=16$

388.

$k-42=113$

389.

$19=p-15$

390.

$501=u-399$

Translate English Sentences to Algebraic Equations

In the following exercises, translate each English sentence into an algebraic equation.

391.

The sum of $7$ and $33$ is equal to $40.$

392.

The difference of $15$ and $3$ is equal to $12.$

393.

The product of $4$ and $8$ is equal to $32.$

394.

The quotient of $63$ and $9$ is equal to $7.$

395.

Twice the difference of $n$ and $3$ gives $76.$

396.

The sum of five times $y$ and $4$ is $89.$

Translate to an Equation and Solve

In the following exercises, translate each English sentence into an algebraic equation and then solve it.

397.

Eight more than $x$ is equal to $35.$

398.

$21$ less than $a$ is $11.$

399.

The difference of $q$ and $18$ is $57.$

400.

The sum of $m$ and $125$ is $240.$

Mixed Practice

In the following exercises, solve each equation.

401.

$h-15=27$

402.

$k-11=34$

403.

$z+52=85$

404.

$x+93=114$

405.

$27=q+19$

406.

$38=p+19$

407.

$31=v-25$

408.

$38=u-16$

Find Multiples and Factors

Identify Multiples of Numbers

In the following exercises, list all the multiples less than $50$ for each of the following.

409.

$3$

410.

$2$

411.

$8$

412.

$10$

Use Common Divisibility Tests

In the following exercises, using the divisibility tests, determine whether each number is divisible by $2,\text{by}3,\text{by}5,\text{by}6,\text{and by}10.$

413.

$96$

414.

$250$

415.

$420$

416.

$625$

Find All the Factors of a Number

In the following exercises, find all the factors of each number.

417.

$30$

418.

$70$

419.

$180$

420.

$378$

Identify Prime and Composite Numbers

In the following exercises, identify each number as prime or composite.

421.

$19$

422.

$51$

423.

$121$

424.

$219$

Prime Factorization and the Least Common Multiple

Find the Prime Factorization of a Composite Number

In the following exercises, find the prime factorization of each number.

425.

$84$

426.

$165$

427.

$350$

428.

$572$

Find the Least Common Multiple of Two Numbers

In the following exercises, find the least common multiple of each pair of numbers.

429.

$9,15$

430.

$12,20$

431.

$25,35$

432.

$18,40$

Everyday Math

433.

Describe how you have used two topics from The Language of Algebra chapter in your life outside of your math class during the past month.