8.4 Solve Equations with Fraction or Decimal Coefficients

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$0.6y+3=9$$

$$0.4y-4=2$$

$$3.6j-2=5.2$$

$$2.1k+3=7.2$$

$$0.4x+0.6=0.5x-1.2$$

$$0.7x+0.4=0.6x+2.4$$

$$0.23x+1.47=0.37x-1.05$$

$$0.48x+1.56=0.58x-0.64$$

$$0.9x-1.25=0.75x+1.75$$

$$1.2x-0.91=0.8x+2.29$$

$$0.05n+0.10(n+8)=2.15$$

$$0.05n+0.10(n+7)=3.55$$

$$0.10d+0.25(d+5)=4.05$$

$$0.10d+0.25(d+7)=5.25$$

$$0.05(q-5)+0.25q=3.05$$

$$0.05(q-8)+0.25q=4.10$$

Coins Taylor has $\text{\$2.00}$ 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.

Stamps Travis bought $\text{\$9.45}$ worth of $\text{49-cent}$ stamps and $\text{21-cent}$ stamps. The number of $\text{21-cent}$ stamps was $5$ less than the number of $\text{49-cent}$ stamps. Solve the equation $0.49s+0.21(s-5)=9.45$ for $s,$ to find the number of $\text{49-cent}$ stamps Travis bought.

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

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

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

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

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

$$w-8=5,w=3$$

$$\mathrm{-9}n=45,n=54$$

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

$$x+7=19$$

$$y+2=\mathrm{-6}$$

$$a+\frac{1}{3}=\frac{5}{3}$$

$$n+3.6=5.1$$

$$u-7=10$$

$$x-9=\mathrm{-4}$$

$$c-\frac{3}{11}=\frac{9}{11}$$

$$p-4.8=14$$

$$n-12=32$$

$$y+16=\mathrm{-9}$$

$$f+\frac{2}{3}=4$$

$$d-3.9=8.2$$

$$y+8-15=\mathrm{-3}$$

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

$$6(n-1)-5n=\mathrm{-14}$$

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

The sum of $\mathrm{-6}$ and $m$ is $25.$

Four less than $n$ is $13.$

Rochelle’s daughter is $11$ years old. Her son is $3$ years younger. How old is her son?

Tan weighs $146$ pounds. Minh weighs $15$ pounds more than Tan. How much does Minh weigh?

Peter paid $\text{\$9.75}$ to go to the movies, which was $\text{\$46.25}$ less than he paid to go to a concert. How much did he pay for the concert?

Elissa earned $\text{\$152.84}$ this week, which was $\text{\$21.65}$ more than she earned last week. How much did she earn last week?

$$8x=72$$

$$13a=\mathrm{-65}$$

$$0.25p=5.25$$

$$-y=4$$

$$\frac{n}{6}=18$$

$$\frac{y}{\mathrm{-10}}=30$$

$$36=\frac{3}{4}x$$

$$\frac{5}{8}u=\frac{15}{16}$$

$$\mathrm{-18}m=\mathrm{-72}$$

$$\frac{c}{9}=36$$

$$0.45x=6.75$$

$$\frac{11}{12}=\frac{2}{3}y$$

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

$$24x+8x-11x=\mathrm{-7}\mathrm{-14}$$

$$8p+7=47$$

$$10w-5=65$$

$$3x+19=\mathrm{-47}$$

$$32=\mathrm{-4}-9n$$

$$7y=6y-13$$

$$5a+21=2a$$

$$k=\mathrm{-6}k-35$$

$$4x-\frac{3}{8}=3x$$

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

$$5n-20=\mathrm{-7}n-80$$

$$4u+16=\mathrm{-19}-u$$

$$\frac{5}{8}c-4=\frac{3}{8}c+4$$

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

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

$$-(s+4)=18$$

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

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

$$\frac{1}{3}(6m+21)=m-7$$

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

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

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

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

$$\frac{2}{5}n-\frac{1}{10}=\frac{7}{10}$$

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

$$\frac{3}{4}a-\frac{1}{3}=\frac{1}{2}a+\frac{5}{6}$$

$$\frac{1}{2}(k+3)=\frac{1}{3}(k+16)$$

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

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

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

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