Respuesta :
QUESTION:
Solve the following equation 2/3 x + 6 = 1/2 x + 1/4x
ANSWER:
In all choices the correct answer is B [tex]\blue{\boxed{72}}[/tex]
STEP-BY-STEP EXPLANATION:
[tex]\blue{\boxed{Note:}}[/tex] Since x is on the right side of the equation, switch the sides so it is on the left side of the equation
[tex] \frac{1}{2} x + \frac{1}{4} x = \frac{2}{3} x + 6[/tex]
First, Simply each term
Combine [tex]{\frac{1}{2}}[/tex], [tex]{\frac{1}{4}}[/tex] to x
[tex] \frac{x}{2} + \frac{x}{4} = \frac{2}{3} x + 6[/tex]
[tex]\blue{\boxed{Note:}}[/tex] To write [tex]{\frac{x}{2}}[/tex] as a fraction with a common denominator, multiply by [tex]{\frac{2}{2}}[/tex]
[tex] \frac{x}{2} \times \frac{2}{2} + \frac{x}{4} = \frac{2}{3} x + 6[/tex]
Second, Write each expression with a common denominator of 4, by multiplying each by appropriate factor of 1
Multiply [tex]{\frac{x}{2}}[/tex] and [tex]{\frac{2}{2}}[/tex]
[tex] \frac{x \times 2}{2 \times 2} + \frac{x}{4} = \frac{2}{3} x + 6[/tex]
Multiply 2 and 2
[tex] \frac{x \times 2}{4} + \frac{x}{4} = \frac{2}{3} x + 6[/tex]
[tex]\blue{\boxed{Note:}}[/tex] Combine the numerators over the common denominator
[tex] \frac{x \times 2 + x}{4} = \frac{2}{3} x + 6[/tex]
Third, Simplify the numerator
Move 2 to the left of x
[tex] \frac{2 \times x + x}{4} = \frac{2}{3} x + 6[/tex]
Add 2x and x
[tex] \frac{3x}{4} = \frac{2}{3} x + 6[/tex]
[tex]\blue{\boxed{Note:}}[/tex] Combine [tex]{\frac{2}{3}}[/tex] and x
[tex] \frac{3x}{4} = \frac{2x}{3} + 6[/tex]
Fourth, Move all terms containing x to the left side of the equation
Subtract [tex]{\frac{2x}{3}}[/tex] from both sides of the equation
[tex] \frac{3x}{4} - \frac{2x}{3} = 6[/tex]
[tex]\blue{\boxed{Note:}}[/tex] To write [tex]{\frac{3x}{4}}[/tex] as a fraction with a common denominator, multiply by [tex]{\frac{3}{3}}[/tex]
[tex] \frac{3x}{4} \times \frac{3}{3} - \frac{2x}{3} = 6[/tex]
[tex]\blue{\boxed{Note Again:}}[/tex] To write [tex]{\frac{-2x}{3}}[/tex] as a fraction with a common denominator, multiply by [tex]{\frac{4}{4}}[/tex]
[tex] \frac{3x}{4} \times \frac{3}{3} - \frac{2x}{3} \times \frac{4}{4} = 6[/tex]
Fifth, Write each expression with a common denominator of 12, by multiplying each by an appropriate factor of 1
Multiply [tex]{\frac{3x}{4}}[/tex] and [tex]{\frac{3}{3}}[/tex]
[tex] \frac{3x \times 3}{4 \times 3} - \frac{2x}{3} \times \frac{4}{4} = 6[/tex]
Multiply 4 and 3
[tex] \frac{3x \times 3}{12} - \frac{2x}{3} \times \frac{4}{4} = 6[/tex]
Multiply [tex]{\frac{2x}{3}}[/tex] and [tex]{\frac{4}{4}}[/tex]
[tex] \frac{3x \times 3}{12} - \frac{2x \times 4}{3 \times 4} = 6[/tex]
Multiply 3 and 4
[tex] \frac{3x \times 3}{12} - \frac{2x \times 4}{12} = 6[/tex]
[tex]\blue{\boxed{Note:}}[/tex] Combine the numerators over the common denominator
[tex] \frac{3x \times 3 - 2x \times 4}{12} = 6[/tex]
Sixth, Simplify the numerator
Factor x out of 3x ×3 - 2x × 4
[tex] \frac{x(3 \times 3 - 2 \times 4)}{12} = 6[/tex]
Multiply 3 by 3
[tex] \frac{x(9 - 2 \times 4)}{12} = 6[/tex]
Multiply - 2 by 4
[tex] \frac{x(9 - 8)}{12} = 6[/tex]
Subtract 8 from 9
[tex] \frac{x \times 1}{12} = 6[/tex]
Multiply x by 1
[tex] \frac{x}{12} = 6[/tex]
[tex]\blue{\boxed{Note:}}[/tex] Multiply both sides of the equation by 12
[tex]12 \times \frac{x}{12} = 12 \times 6[/tex]
Seventh, Simplify both sides of the equation and cancel the common factor of 12
Cancel the common factor
[tex]12 \times \frac{x}{12} = 12 \times 6[/tex]
Rewrite the expression
[tex]x = 12 \times 6[/tex]
Lastly, Multiply 12 by 6
[tex]\blue{\boxed{ x = 72}}[/tex]
hope it's helps
