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Basic Numeracy/Quantitative Aptitude

Detailed Solution

150.

151. c: given 2(-4a - 5b) - (8 + b) + b + (-2b + 4) - 5a
multiply factors
-8a - 10b - 8 - b + b -2b + 4 - 5a
group like terms
- 13a - 12b - 4

152. d: given 2(-3x - 5) - (8 - x) = -2(2x + 4) + 12
multiply factors
-6x -10 - 8 + x = -4x - 8 + 12
group like terms
-5x - 18 = -4x + 4
add 18 to both sides
-5x -18 + 18 = -4x + 4 + 18
group like terms
-5x = -4x + 22
add 4x to both sides
-5x + 4x = -4x + 22 +4x
group like terms
-x = 22
multiply both sides by -1
x = -22
Check the solution
left side:2(-3*(-22) - 5) - (8 - (-22)) = 92
right side:-2(2(-22) +4) + 12 = 92
Conclusion
x = -22 is the solution to the given equation

153. c: To simplify the given expression, we need to simplify the terms with absolute value using definition of absolute value.
if x > = 0 , | x | = x
if x < 0 , | x | = -x
According to the definition of the absolute value above, x > - 2 (given above) is equivalent to x + 2 > 0
if x + 2 > 0 then | x + 2 | = x + 2
the above definition gives
| 6 - 9 | = | - 3 | = 3
the whole expression given above can now be written as 2(x + 2) - 3x - (-2 - x) + 3
multiply factor
2x + 4 -3x + 2 + x + 3
group like terms
9

154. c: We first write the equation in slope intercept form y = mx +b. Put terms in x and constant terms on the right side
2y = 3x + 10
Divide both sides by 2
y = (3/2)x + 5
Now that the equation is in slope intercept form, we identify the slope as the coefficient of x and is equal to 3/2 and the y intercept as (0 , 5).


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