Prealgebra

# Review Exercises

PrealgebraReview Exercises

### Review Exercises

##### Solve Equations using the Subtraction and Addition Properties of Equality

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

255.

$x + 16 = 31 , x = 15 x + 16 = 31 , x = 15$

256.

$w − 8 = 5 , w = 3 w − 8 = 5 , w = 3$

257.

$−9 n = 45 , n = 54 −9 n = 45 , n = 54$

258.

$4 a = 72 , a = 18 4 a = 72 , a = 18$

In the following exercises, solve the equation using the Subtraction Property of Equality.

259.

$x + 7 = 19 x + 7 = 19$

260.

$y + 2 = −6 y + 2 = −6$

261.

$a + 1 3 = 5 3 a + 1 3 = 5 3$

262.

$n + 3.6 = 5.1 n + 3.6 = 5.1$

In the following exercises, solve the equation using the Addition Property of Equality.

263.

$u − 7 = 10 u − 7 = 10$

264.

$x − 9 = −4 x − 9 = −4$

265.

$c − 3 11 = 9 11 c − 3 11 = 9 11$

266.

$p − 4.8 = 14 p − 4.8 = 14$

In the following exercises, solve the equation.

267.

$n − 12 = 32 n − 12 = 32$

268.

$y + 16 = −9 y + 16 = −9$

269.

$f + 2 3 = 4 f + 2 3 = 4$

270.

$d − 3.9 = 8.2 d − 3.9 = 8.2$

271.

$y + 8 − 15 = −3 y + 8 − 15 = −3$

272.

$7 x + 10 − 6 x + 3 = 5 7 x + 10 − 6 x + 3 = 5$

273.

$6 ( n − 1 ) − 5 n = −14 6 ( n − 1 ) − 5 n = −14$

274.

$8 ( 3 p + 5 ) − 23 ( p − 1 ) = 35 8 ( 3 p + 5 ) − 23 ( p − 1 ) = 35$

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

275.

The sum of $−6−6$ and $mm$ is $25.25.$

276.

Four less than $nn$ is $13.13.$

In the following exercises, translate into an algebraic equation and solve.

277.

Rochelle’s daughter is $1111$ years old. Her son is $33$ years younger. How old is her son?

278.

Tan weighs $146146$ pounds. Minh weighs $1515$ pounds more than Tan. How much does Minh weigh?

279.

Peter paid $9.759.75$ to go to the movies, which was $46.2546.25$ less than he paid to go to a concert. How much did he pay for the concert?

280.

Elissa earned $152.84152.84$ this week, which was $21.6521.65$ more than she earned last week. How much did she earn last week?

##### Solve Equations using the Division and Multiplication Properties of Equality

In the following exercises, solve each equation using the Division Property of Equality.

281.

$8 x = 72 8 x = 72$

282.

$13 a = −65 13 a = −65$

283.

$0.25 p = 5.25 0.25 p = 5.25$

284.

$− y = 4 − y = 4$

In the following exercises, solve each equation using the Multiplication Property of Equality.

285.

$n 6 = 18 n 6 = 18$

286.

$y −10 = 30 y −10 = 30$

287.

$36 = 3 4 x 36 = 3 4 x$

288.

$5 8 u = 15 16 5 8 u = 15 16$

In the following exercises, solve each equation.

289.

$−18 m = −72 −18 m = −72$

290.

$c 9 = 36 c 9 = 36$

291.

$0.45 x = 6.75 0.45 x = 6.75$

292.

$11 12 = 2 3 y 11 12 = 2 3 y$

293.

$5 r − 3 r + 9 r = 35 − 2 5 r − 3 r + 9 r = 35 − 2$

294.

$24 x + 8 x − 11 x = −7 −14 24 x + 8 x − 11 x = −7 −14$

##### Solve Equations with Variables and Constants on Both Sides

In the following exercises, solve the equations with constants on both sides.

295.

$8 p + 7 = 47 8 p + 7 = 47$

296.

$10 w − 5 = 65 10 w − 5 = 65$

297.

$3 x + 19 = −47 3 x + 19 = −47$

298.

$32 = −4 − 9 n 32 = −4 − 9 n$

In the following exercises, solve the equations with variables on both sides.

299.

$7 y = 6 y − 13 7 y = 6 y − 13$

300.

$5 a + 21 = 2 a 5 a + 21 = 2 a$

301.

$k = −6 k − 35 k = −6 k − 35$

302.

$4 x − 3 8 = 3 x 4 x − 3 8 = 3 x$

In the following exercises, solve the equations with constants and variables on both sides.

303.

$12 x − 9 = 3 x + 45 12 x − 9 = 3 x + 45$

304.

$5 n − 20 = −7 n − 80 5 n − 20 = −7 n − 80$

305.

$4 u + 16 = −19 − u 4 u + 16 = −19 − u$

306.

$5 8 c − 4 = 3 8 c + 4 5 8 c − 4 = 3 8 c + 4$

In the following exercises, solve each linear equation using the general strategy.

307.

$6 ( x + 6 ) = 24 6 ( x + 6 ) = 24$

308.

$9 ( 2 p − 5 ) = 72 9 ( 2 p − 5 ) = 72$

309.

$− ( s + 4 ) = 18 − ( s + 4 ) = 18$

310.

$8 + 3 ( n − 9 ) = 17 8 + 3 ( n − 9 ) = 17$

311.

$23 − 3 ( y − 7 ) = 8 23 − 3 ( y − 7 ) = 8$

312.

$1 3 ( 6 m + 21 ) = m − 7 1 3 ( 6 m + 21 ) = m − 7$

313.

$8 ( r − 2 ) = 6 ( r + 10 ) 8 ( r − 2 ) = 6 ( r + 10 )$

314.

$5 + 7 ( 2 − 5 x ) = 2 ( 9 x + 1 ) − ( 13 x − 57 ) 5 + 7 ( 2 − 5 x ) = 2 ( 9 x + 1 ) − ( 13 x − 57 )$

315.

$4 ( 3.5 y + 0.25 ) = 365 4 ( 3.5 y + 0.25 ) = 365$

316.

$0.25 ( q − 8 ) = 0.1 ( q + 7 ) 0.25 ( q − 8 ) = 0.1 ( q + 7 )$

##### Solve Equations with Fraction or Decimal Coefficients

In the following exercises, solve each equation by clearing the fractions.

317.

$2 5 n − 1 10 = 7 10 2 5 n − 1 10 = 7 10$

318.

$1 3 x + 1 5 x = 8 1 3 x + 1 5 x = 8$

319.

$3 4 a − 1 3 = 1 2 a + 5 6 3 4 a − 1 3 = 1 2 a + 5 6$

320.

$1 2 ( k + 3 ) = 1 3 ( k + 16 ) 1 2 ( k + 3 ) = 1 3 ( k + 16 )$

In the following exercises, solve each equation by clearing the decimals.

321.

$0.8 x − 0.3 = 0.7 x + 0.2 0.8 x − 0.3 = 0.7 x + 0.2$

322.

$0.36 u + 2.55 = 0.41 u + 6.8 0.36 u + 2.55 = 0.41 u + 6.8$

323.

$0.6 p − 1.9 = 0.78 p + 1.7 0.6 p − 1.9 = 0.78 p + 1.7$

324.

$0.10 d + 0.05 ( d − 4 ) = 2.05 0.10 d + 0.05 ( d − 4 ) = 2.05$

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