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Math  /  Algebra

Question40. [-/1 Points] DETAILS MY NOTES EWENMATH12 6.4.001. 0/100 Submissions Used
ASK YOUR TEACHER
Solve the equation and check. x=□2x3=246x=\square \frac{2 x}{3}=\frac{24}{6}

Studdy Solution

STEP 1

1. The equation involves a variable x x that we need to solve for.
2. The equation given is 2x3=246 \frac{2x}{3} = \frac{24}{6} .
3. Basic algebraic operations such as multiplication, division, and simplification of fractions will be used to solve the equation.

STEP 2

1. Simplify the right-hand side of the equation.
2. Solve for x x by isolating it on one side of the equation.
3. Verify the solution by substituting it back into the original equation.

STEP 3

Simplify the right-hand side of the equation 246 \frac{24}{6} .
246=4\frac{24}{6} = 4

STEP 4

Rewrite the equation with the simplified right-hand side.
2x3=4\frac{2x}{3} = 4

STEP 5

To isolate x x , multiply both sides of the equation by 3 to eliminate the fraction.
2x=4×32x = 4 \times 3
2x=122x = 12

STEP 6

Divide both sides by 2 to solve for x x .
x=122x = \frac{12}{2}
x=6x = 6

STEP 7

Verify the solution by substituting x=6 x = 6 back into the original equation.
Substitute x=6 x = 6 into 2x3 \frac{2x}{3} :
2×63=123=4\frac{2 \times 6}{3} = \frac{12}{3} = 4
Since the left-hand side equals the right-hand side of the original equation, the solution is verified.
The solution to the equation is:
x=6x = 6

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