Question

Which expression is equivalent to 2/3 (9x - 6) + 4 (1/2x - 1/2)

Answer 1

Answer:

Given expression $\frac{2}{3}(9x-6)+4(\frac{1}{2}x-\frac{1}{2})$ is equivalent to the expression $2(4x-3)$.

Step-by-step explanation:

Given expression is  $\frac{2}{3}(9x-6)+4(\frac{1}{2}x-\frac{1}{2})$

To simplify the expression:

$\frac{2}{3}(9x-6)+4(\frac{1}{2}x-\frac{1}{2})=\frac{18x-12}{3}+\frac{4x-4}{2}$

Taking LCM 6 to the above expression we get

$=\frac{(18x-12)2+3(4x-4)}{6}$ (Applying multiplication rules)

$=\frac{36x-24+12x-12}{6}$  ( doing sums to the terms)

$=\frac{48x-36}{6}$

$=8x-6$

We can take common number 2 outside to the above expression

$=2(4x-3)$

Therefore  $\frac{2}{3}(9x-6)+4(\frac{1}{2}x-\frac{1}{2})=2(4x-3)$

Therefore given expression $\frac{2}{3}(9x-6)+4(\frac{1}{2}x-\frac{1}{2})$ is equivalent to the expression $2(4x-3)$

Answer 2

$\frac{2}{3}(9x-6)+4(\frac{1}{2}x-\frac{1}{2})$ is equivalent to $8x-6$

Step-by-step explanation:

We need to find Which expression is equivalent to $\frac{2}{3}(9x-6)+4(\frac{1}{2}x-\frac{1}{2})$

Solving:

Multiply 2/3 with terms inside the bracket and 4 with terms inside the bracket.

$\frac{2}{3}(9x-6)+4(\frac{1}{2}x-\frac{1}{2})$

$=\frac{2}{3}(9x)-\frac{2}{3}(6)+4(\frac{1}{2}x)-4(\frac{1}{2})$

Simplifying:

$=2(3x)-2(2)+2(x)-2(1)\\=6x-4+2x-2\\Combining\,\,like\,\,terms:\\=8x-6$

So, $\frac{2}{3}(9x-6)+4(\frac{1}{2}x-\frac{1}{2})$ is equivalent to $8x-6$

Keywords: Solving Fractions  

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