If 1/2 the result obtained when 2 is subtracted from 5 x...

Question

If 1/2 the result obtained when 2 is subtracted from 5 x is equal to the sum of 10 and 3 x, what is the value of x ?

GMAT Panda · Accepted Answer

-22 We translate "the result obtained when 2 is subtracted from 5x" into a subtraction expression. 5x - 2 We translate "half the result obtained when 2 is subtracted from 5x" into a fractional expression. 1/2(5x - 2) We translate "the sum of 10 and 3x" into an addition expression. 10 + 3x We form the equation by translating "is equal to". 1/2(5x - 2) = 10 + 3x We multiply both sides by 2 to remove the fraction. 5x - 2 = 2 (10 + 3x) We distribute the 2 on the right side. 5x - 2 = 20 + 6x We subtract 5x from both sides to group like terms. -2 = 20 + x We subtract 20 from both sides to isolate x. -22 = x

Explanation	Calculations	Help
$We translate "the result obtained when 2 is subtracted from 5x" into a subtraction expression.$	$5 x - 2$
$We translate into a fractional expression.$	$\frac{1}{2} (5 x - 2)$
$We translate "the sum of 10 and 3x" into an addition expression.$	$10 + 3 x$
$We form the equation by translating "is equal to" .$	$\frac{1}{2} (5 x - 2) = 10 + 3 x$
$We multiply both sides by 2 to remove the fraction.$	$5 x - 2 = 2 \times (10 + 3 x)$
$We distribute the 2 on the right side.$	$5 x - 2 = 20 + 6 x$
$We subtract 5 x from both sides to group like terms.$	$- 2 = 20 + x$
$We subtract 20 from both sides to isolate x .$	$- 22 = x$

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