 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.

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

256.

$w−8=5,w=3w−8=5,w=3$

257.

$−9n=45,n=54−9n=45,n=54$

258.

$4a=72,a=184a=72,a=18$

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

259.

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

260.

$y+2=−6y+2=−6$

261.

$a+13=53a+13=53$

262.

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

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

263.

$u−7=10u−7=10$

264.

$x−9=−4x−9=−4$

265.

$c−311=911c−311=911$

266.

$p−4.8=14p−4.8=14$

In the following exercises, solve the equation.

267.

$n−12=32n−12=32$

268.

$y+16=−9y+16=−9$

269.

$f+23=4f+23=4$

270.

$d−3.9=8.2d−3.9=8.2$

271.

$y+8−15=−3y+8−15=−3$

272.

$7x+10−6x+3=57x+10−6x+3=5$

273.

$6(n−1)−5n=−146(n−1)−5n=−14$

274.

$8(3p+5)−23(p−1)=358(3p+5)−23(p−1)=35$

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.

$8x=728x=72$

282.

$13a=−6513a=−65$

283.

$0.25p=5.250.25p=5.25$

284.

$−y=4−y=4$

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

285.

$n6=18n6=18$

286.

$y−10=30y−10=30$

287.

$36=34x36=34x$

288.

$58u=151658u=1516$

In the following exercises, solve each equation.

289.

$−18m=−72−18m=−72$

290.

$c9=36c9=36$

291.

$0.45x=6.750.45x=6.75$

292.

$1112=23y1112=23y$

293.

$5r−3r+9r=35−25r−3r+9r=35−2$

294.

$24x+8x−11x=−7−1424x+8x−11x=−7−14$

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

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

295.

$8p+7=478p+7=47$

296.

$10w−5=6510w−5=65$

297.

$3x+19=−473x+19=−47$

298.

$32=−4−9n32=−4−9n$

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

299.

$7y=6y−137y=6y−13$

300.

$5a+21=2a5a+21=2a$

301.

$k=−6k−35k=−6k−35$

302.

$4x−38=3x4x−38=3x$

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

303.

$12x−9=3x+4512x−9=3x+45$

304.

$5n−20=−7n−805n−20=−7n−80$

305.

$4u+16=−19−u4u+16=−19−u$

306.

$58c−4=38c+458c−4=38c+4$

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

307.

$6(x+6)=246(x+6)=24$

308.

$9(2p−5)=729(2p−5)=72$

309.

$−(s+4)=18−(s+4)=18$

310.

$8+3(n−9)=178+3(n−9)=17$

311.

$23−3(y−7)=823−3(y−7)=8$

312.

$13(6m+21)=m−713(6m+21)=m−7$

313.

$8(r−2)=6(r+10)8(r−2)=6(r+10)$

314.

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

315.

$4(3.5y+0.25)=3654(3.5y+0.25)=365$

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.

$25n−110=71025n−110=710$

318.

$13x+15x=813x+15x=8$

319.

$34a−13=12a+5634a−13=12a+56$

320.

$12(k+3)=13(k+16)12(k+3)=13(k+16)$

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

321.

$0.8x−0.3=0.7x+0.20.8x−0.3=0.7x+0.2$

322.

$0.36u+2.55=0.41u+6.80.36u+2.55=0.41u+6.8$

323.

$0.6p−1.9=0.78p+1.70.6p−1.9=0.78p+1.7$

324.

$0.10d+0.05(d−4)=2.050.10d+0.05(d−4)=2.05$

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