Solving One-Step Equations

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Algebra 1

One-Variable Equations

Solving One-Step Equations expand_more

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Exercise 1.6 - Solution

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a

To solve the equation we have to isolate $a$ on one side. By adding $\frac{1}{2}$ to both sides of the equality, $a$ will be standing alone on the left-hand side.

$\text{-}\frac{1}{2}+a=\frac{5}{8}$

AddEqn$\text{LHS}+\frac{1}{2}=\text{RHS}+\frac{1}{2}$

$a=\frac{5}{8}+\frac{1}{2}$

ExpandFrac$\frac{a}{b}=\frac{a\cdot 4}{b\cdot 4}$

$a=\frac{5}{8}+\frac{4}{8}$

AddFracAdd fractions

$a=\frac{9}{8}$

b

To solve the equation we have to isolate $w$ on one side. Thus, we want to cancel out $\frac{2}{5}$ by subtracting it from both sides.

$\frac{3}{4}=w+\frac{2}{5}$

SubEqn$\text{LHS}-\frac{2}{5}=\text{RHS}-\frac{2}{5}$

$\frac{3}{4}-\frac{2}{5}=w$

RearrangeEqnRearrange equation

$w=\frac{3}{4}-\frac{2}{5}$

To subtract the fractions they need to have the same denominator. Here, the lowest common denominator is $20.$

$w=\frac{3}{4}-\frac{2}{5}$

ExpandFrac$\frac{a}{b}=\frac{a\cdot 5}{b\cdot 5}$

$w=\frac{3\cdot 5}{4\cdot 5}-\frac{2}{5}$

ExpandFrac$\frac{a}{b}=\frac{a\cdot 4}{b\cdot 4}$

$w=\frac{3\cdot 5}{4\cdot 5}-\frac{2\cdot 4}{5\cdot 4}$

MultiplyMultiply

$w=\frac{15}{20}-\frac{8}{20}$

SubFracSubtract fractions

$w=\frac{7}{20}$

c

To isolate $k$ we want to multiply both sides with $5$ as it's the inverse operation of dividing by $5.$

$\text{-}\frac{k}{5}=\frac{7}{10}$

MultEqn$\text{LHS}\cdot 5=\text{RHS}\cdot 5$

$\text{-}k=\frac{7}{10}\cdot 5$

MoveRightFacToNum$\frac{a}{c}\cdot b=\frac{a\cdot b}{c}$

$\text{-}k=\frac{35}{10}$

ChangeSignsChange signs

$k=\text{-}\frac{35}{10}$

ReduceFrac$\frac{a}{b}=\frac{a/5}{b/5}$

$k=\text{-}\frac{7}{2}$