2.5 Solve Equations with Fractions or Decimals - Elementary Algebra 2e | OpenStax (2024)

318.

$\frac{1}{4}x-\frac{1}{2}=-\frac{3}{4}$

319.

$\frac{3}{4}x-\frac{1}{2}=\frac{1}{4}$

320.

$\frac{5}{6}y-\frac{2}{3}=-\frac{3}{2}$

321.

$\frac{5}{6}y-\frac{1}{3}=-\frac{7}{6}$

322.

$\frac{1}{2}a+\frac{3}{8}=\frac{3}{4}$

323.

$\frac{5}{8}b+\frac{1}{2}=-\frac{3}{4}$

324.

$2=\frac{1}{3}x-\frac{1}{2}x+\frac{2}{3}x$

325.

$2=\frac{3}{5}x-\frac{1}{3}x+\frac{2}{5}x$

326.

$\frac{1}{4}m-\frac{4}{5}m+\frac{1}{2}m=\mathrm{-1}$

327.

$\frac{5}{6}n-\frac{1}{4}n-\frac{1}{2}n=\mathrm{-2}$

328.

$x+\frac{1}{2}=\frac{2}{3}x-\frac{1}{2}$

329.

$x+\frac{3}{4}=\frac{1}{2}x-\frac{5}{4}$

330.

$\frac{1}{3}w+\frac{5}{4}=w-\frac{1}{4}$

331.

$\frac{3}{2}z+\frac{1}{3}=z-\frac{2}{3}$

332.

$\frac{1}{2}x-\frac{1}{4}=\frac{1}{12}x+\frac{1}{6}$

333.

$\frac{1}{2}a-\frac{1}{4}=\frac{1}{6}a+\frac{1}{12}$

334.

$\frac{1}{3}b+\frac{1}{5}=\frac{2}{5}b-\frac{3}{5}$

335.

$\frac{1}{3}x+\frac{2}{5}=\frac{1}{5}x-\frac{2}{5}$

336.

$1=\frac{1}{6}\left(12x-6\right)$

337.

$1=\frac{1}{5}\left(15x-10\right)$

338.

$\frac{1}{4}\left(p-7\right)=\frac{1}{3}\left(p+5\right)$

339.

$\frac{1}{5}\left(q+3\right)=\frac{1}{2}\left(q-3\right)$

340.

$\frac{1}{2}\left(x+4\right)=\frac{3}{4}$

341.

$\frac{1}{3}\left(x+5\right)=\frac{5}{6}$

342.

$\frac{5q-8}{5}=\frac{2q}{10}$

343.

$\frac{4m+2}{6}=\frac{m}{3}$

344.

$\frac{4n+8}{4}=\frac{n}{3}$

345.

$\frac{3p+6}{3}=\frac{p}{2}$

346.

$\frac{u}{3}-4=\frac{u}{2}-3$

347.

$\frac{v}{10}+1=\frac{v}{4}-2$

348.

$\frac{c}{15}+1=\frac{c}{10}-1$

349.

$\frac{d}{6}+3=\frac{d}{8}+2$

350.

$\frac{3x+4}{2}+1=\frac{5x+10}{8}$

351.

$\frac{10y-2}{3}+3=\frac{10y+1}{9}$

352.

$\frac{7u-1}{4}-1=\frac{4u+8}{5}$

353.

$\frac{3v-6}{2}+5=\frac{11v-4}{5}$

354.

$0.6y+3=9$

355.

$0.4y-4=2$

356.

$3.6j-2=5.2$

357.

$2.1k+3=7.2$

358.

$0.4x+0.6=0.5x-1.2$

359.

$0.7x+0.4=0.6x+2.4$

360.

$0.23x+1.47=0.37x-1.05$

361.

$0.48x+1.56=0.58x-0.64$

362.

$0.9x-1.25=0.75x+1.75$

363.

$1.2x-0.91=0.8x+2.29$

364.

$0.05n+0.10\left(n+8\right)=2.15$

365.

$0.05n+0.10\left(n+7\right)=3.55$

366.

$0.10d+0.25\left(d+5\right)=4.05$

367.

$0.10d+0.25\left(d+7\right)=5.25$

368.

$0.05\left(q-5\right)+0.25q=3.05$

369.

$0.05\left(q-8\right)+0.25q=4.10$

370.

Coins Taylor has $2.00 in dimes and pennies. The number of pennies is 2 more than the number of dimes. Solve the equation $0.10d+0.01(d+2)=2$ for $d$, the number of dimes.

371.

Stamps Paula bought $22.82 worth of 49-cent stamps and 21-cent stamps. The number of 21-cent stamps was 8 less than the number of 49-cent stamps. Solve the equation $0.49s+0.21(s-8)=22.82$ for s, to find the number of 49-cent stamps Paula bought.

372.

Explain how you find the least common denominator of $\frac{3}{8}$, $\frac{1}{6}$, and $\frac{2}{3}$.

373.

If an equation has several fractions, how does multiplying both sides by the LCD make it easier to solve?

374.

If an equation has fractions only on one side, why do you have to multiply both sides of the equation by the LCD?

375.

In the equation $0.35x+2.1=3.85$ what is the LCD? How do you know?