GMAT Linear Equations Explained — \frac{1}{2} the result obtained when 2 is subtracted from 5 x...

If \frac{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 ?

linear equationstranslations

Explanation	Calculations	Help
$We translate "the result obtained when 2 is subtracted from 5x" into a subtraction expression.$	$5 x - 2$	Theory & Tactics Method Card TRANS1-D Click to view full details
$We translate into a fractional expression.$	$\frac{1}{2} (5 x - 2)$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We translate "the sum of 10 and 3x" into an addition expression.$	$10 + 3 x$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We form the equation by translating "is equal to" .$	$\frac{1}{2} (5 x - 2) = 10 + 3 x$	Theory & Tactics Method Card TRANS1-B Click to view full details
$We multiply both sides by 2 to remove the fraction.$	$5 x - 2 = 2 \times (10 + 3 x)$	Theory & Tactics Method Card EQUA1-A Click to view full details
$We distribute the 2 on the right side.$	$5 x - 2 = 20 + 6 x$	Theory & Tactics Method Card EQUA1-A Click to view full details
$We subtract 5 x from both sides to group like terms.$	$- 2 = 20 + x$	Theory & Tactics Method Card EQUA1-B Click to view full details
$We subtract 20 from both sides to isolate x .$	$- 22 = x$	Theory & Tactics Method Card EQUA1-C Click to view full details

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