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Math  /  Algebra

Questionx−23=79x-\frac{2}{3}=\frac{7}{9}

Studdy Solution

STEP 1

1. The equation x−23=79 x - \frac{2}{3} = \frac{7}{9} is asking us to solve for x x .
2. This is a one-step equation with one solution.
3. The equation involves fractions and basic algebraic operations.

STEP 2

1. Isolate the variable x x by performing algebraic operations.
2. Check the solution by substituting it back into the original equation.

STEP 3

To isolate x x , we need to eliminate the fraction 23 \frac{2}{3} from the left side of the equation. We do this by adding 23 \frac{2}{3} to both sides of the equation:
x−23+23=79+23 x - \frac{2}{3} + \frac{2}{3} = \frac{7}{9} + \frac{2}{3}

STEP 4

Simplify the left side:
x=79+23 x = \frac{7}{9} + \frac{2}{3}
To add the fractions on the right side, find a common denominator. The least common denominator of 9 and 3 is 9.
Convert 23 \frac{2}{3} to have a denominator of 9:
23=2×33×3=69 \frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9}
Now add the fractions:
x=79+69=139 x = \frac{7}{9} + \frac{6}{9} = \frac{13}{9}

STEP 5

Check the solution by substituting x=139 x = \frac{13}{9} back into the original equation:
139−23=79 \frac{13}{9} - \frac{2}{3} = \frac{7}{9}
Convert 23 \frac{2}{3} to have a denominator of 9:
23=69 \frac{2}{3} = \frac{6}{9}
Now perform the subtraction:
139−69=79 \frac{13}{9} - \frac{6}{9} = \frac{7}{9}
Both sides are equal, confirming the solution is correct.
The solution is:
139 \boxed{\frac{13}{9}}

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