Question

now we can use the division principle to solve equations even when the answer is not an integer. solve each equation. write your answer as a fraction or as a mixed number.$7x = -25LXB09x = 40LXB12x - 5 = 14LXB2-5x + 1 = 15LXB3-2(x - 5) = 7LXB4x = -2.5LXB5\frac{-2x}{5} = 7LXB6x - 9 = 6x + 7LXB73(x - 5) = x - 20LXB82(x - 3) + x = 9$

Explanation:

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First Section (Fraction/Mixed Number Answers)

Step1: Isolate $x$ (divide by 9)

$9x=40 \implies x=\frac{40}{9}$

Step2: Rewrite as mixed number

$\frac{40}{9}=4\frac{4}{9}$

Step1: Isolate $x$ (divide by -4)

$-4x=17 \implies x=-\frac{17}{4}$

Step2: Rewrite as mixed number

$-\frac{17}{4}=-4\frac{1}{4}$

Step1: Add 5 to both sides

$2x-5=14 \implies 2x=14+5=19$

Step2: Divide by 2

$x=\frac{19}{2}=9\frac{1}{2}$

Step1: Subtract 7 from both sides

$3x+7=-4 \implies 3x=-4-7=-11$

Step2: Divide by 3

$x=-\frac{11}{3}=-3\frac{2}{3}$

Step1: Subtract 1 from both sides

$-5x+1=15 \implies -5x=15-1=14$

Step2: Divide by -5

$x=-\frac{14}{5}=-2\frac{4}{5}$

Step1: Group $x$ terms on one side

$x-3=8x+5 \implies x-8x=5+3$

Step2: Simplify and solve for $x$

$-7x=8 \implies x=-\frac{8}{7}=-1\frac{1}{7}$

Step1: Distribute -2

$-2(x-5)=7 \implies -2x+10=7$

Step2: Subtract 10, divide by -2

$-2x=7-10=-3 \implies x=\frac{3}{2}=1\frac{1}{2}$

Step1: Combine $x$ terms

$x-5x+7=-8 \implies -4x+7=-8$

Step2: Subtract 7, divide by -4

$-4x=-8-7=-15 \implies x=\frac{15}{4}=3\frac{3}{4}$

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Second Section (Decimal Answers)

Step1: Isolate $x$ (divide by -5)

$-5x=18 \implies x=-\frac{18}{5}$

Step2: Convert to decimal

$x=-3.6$

Step1: Multiply by 5, isolate $x$

$\frac{-2x}{5}=7 \implies -2x=35$

Step2: Divide by -2

$x=-\frac{35}{2}=-17.5$

Step1: Group $x$ terms, add 7

$7x-7=3x+20 \implies 7x-3x=20+7$

Step2: Simplify and solve

$4x=27 \implies x=\frac{27}{4}=6.75$

Step1: Group $x$ terms, add 9

$x-9=6x+7 \implies x-6x=7+9$

Step2: Simplify and solve

$-5x=16 \implies x=-\frac{16}{5}=-3.2$

Step1: Multiply by 5, add 2

$\frac{10x-2}{5}=3 \implies 10x-2=15 \implies 10x=17$

Step2: Divide by 10

$x=\frac{17}{10}=1.7$

Step1: Distribute 3, group $x$ terms

$3(x-5)=x-20 \implies 3x-15=x-20 \implies 3x-x=-20+15$

Step2: Simplify and solve

$2x=-5 \implies x=-\frac{5}{2}=-2.5$

Step1: Distribute 4, subtract 24

$4(x+6)=23 \implies 4x+24=23 \implies 4x=23-24=-1$

Step2: Divide by 4

$x=-\frac{1}{4}=-0.25$

Step1: Distribute 2, combine terms

$2(x-3)+x=9 \implies 2x-6+x=9 \implies 3x-6=9$

Step2: Add 6, divide by 3

$3x=15 \implies x=5$
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Answer:

First Section (Fraction/Mixed Number)

1. $9x=40$: $\boldsymbol{x=4\frac{4}{9}}$
2. $-4x=17$: $\boldsymbol{x=-4\frac{1}{4}}$
3. $2x-5=14$: $\boldsymbol{x=9\frac{1}{2}}$
4. $3x+7=-4$: $\boldsymbol{x=-3\frac{2}{3}}$
5. $-5x+1=15$: $\boldsymbol{x=-2\frac{4}{5}}$
6. $x-3=8x+5$: $\boldsymbol{x=-1\frac{1}{7}}$
7. $-2(x-5)=7$: $\boldsymbol{x=1\frac{1}{2}}$
8. $x-5x+7=-8$: $\boldsymbol{x=3\frac{3}{4}}$

Second Section (Decimal)

1. $-5x=18$: $\boldsymbol{x=-3.6}$
2. $\frac{-2x}{5}=7$: $\boldsymbol{x=-17.5}$
3. $7x-7=3x+20$: $\boldsymbol{x=6.75}$
4. $x-9=6x+7$: $\boldsymbol{x=-3.2}$
5. $\frac{10x-2}{5}=3$: $\boldsymbol{x=1.7}$
6. $3(x-5)=x-20$: $\boldsymbol{x=-2.5}$
7. $4(x+6)=23$: $\boldsymbol{x=-0.25}$
8. $2(x-3)+x=9$: $\boldsymbol{x=5}$