1.
A number decreased by 9 equals 4 times the number. Find the number.
Solution: Let m be the required number.m - 9 = 4m [Write the equation.]m - 9 - m = 4m - m [Subtracting m from the two sides of the equation.] -9 = 3m [Simplify.]-9 3 = 3m 3 [Divide throughout by 3.] -3 = m The required number is -3.Correct answer : (4)
2.
What is the value of $x$ , if 2($x$ - 2) + 9 = 3$x$ + 16 ?
Solution: 2(x - 2) + 9 = 3x + 16 2x - 4 + 9 = 3x + 16 [Simplify the terms inside the brackets.] 2x + 5 - 5 = 3x + 16 - 5 [Group the like terms and simplify.] 2x = 3x + 11 [Simplify.] 2x - 3x = 3x + 11 - 3x [Subtracting 3x from the two sides of the equation.] -x = 11 [Simplify.]
x = -11 [Multiply with -1 on both sides.]Correct answer : (2)
3.
Which of the following choices is the solution for the equation $\frac{\mathrm{n}}{\mathrm{(-3)}}$ = 6?
Solution: n (-3) = 6 (- 3) × n (-3) = (- 3) × 6 [Multiply throughout by - 3.]n = - 18 [Simplify.]Correct answer : (4)
4.
Find the value of $m$ , if $m$ + $4\frac{1}{5}$ = $6\frac{1}{7}$ .
Solution: m + 4 1 / 5 = 6 1 / 7 m + 21 / 5 = 43 / 7 [Change to an improper fraction.]m + 21 / 5 - 21 / 5 = 43 / 7 - 21 / 5 [Subtracting 21 / 5 from the two sides of the equation.]m = 68 / 35 [Simplify.]m = 1 33 / 35 [Change to a mixed fraction.]Correct answer : (2)
5.
Solve for $y$ : 8$y$ + $\frac{4}{5}$ = 5$y$ - 4
Solution: 8y + 4 / 5 = 5y - 4 3y + 4 / 5 = - 4 [Subtract 5y from the two sides of the equation.] 3y = - 4 - 4 / 5 [Subtract 4 / 5 from the two sides of the equation.] 3y = - 24 / 5 [Simplify.]y = - 8 / 5 [Divide throughout by 3.]Correct answer : (1)
6.
Solve for $x$ : $x$ + $\frac{x}{13}$ + $\frac{x}{8}$ = 125
Solution: x + x 1 3 + x 8 = 125x (1 + 1 / 8 + 1 / 13 ) = 125x (104 / 104 + 13 / 104 + 8 / 104 ) = 125 [Write equivalent fractions for 1, 1 / 8 and 1 / 13 .]
x ( 125 / 104 ) = 125 [Add.]x 1 0 4 = 1 [Divide throughout by 125.]x = 104 [Multiply throughout by 104.]Correct answer : (4)
7.
Solve for $w$ : $w$ + $\frac{w}{2}$ + $\frac{w}{6}$ - $\frac{w}{3}$ = - $\frac{1}{15}$
Solution: w + w 2 + w 6 - w 3 = - 1 / 15 w (1 + 1 / 2 + 1 / 6 - 1 / 3 ) = - 1 / 15 w ( 6 / 6 + 3 / 6 + 1 / 6 - 2 / 6 ) = - 1 / 15 [Write equivalent fractions for 1, 1 / 2 , 1 / 6 and 1 / 3 .]w (8 / 6 ) = - 1 / 15 [Simplify.] So, w = - 1 / 20 Correct answer : (2)
8.
Solve for $m$ : 9 + 9(- $m$ + 6) = 15$m$ - 7(8 + $m$ )
Solution: 9 + 9(- m + 6) = 15m - 7(8 + m ) 9 - 9m + 54 = 15m - 56 - 7m [Use the distributive property.] 63 - 9m = 8m - 56 [Simplify.] 63 - 17m = - 56 [Subtract 8m from the two sides of the equation.] - 17m = - 119 [Subtract 63 from the two sides of the equation.]m = 7 [Divide throughout by - 17.]Correct answer : (1)
9.
Solve: 2$x$ + 5 + 2(2 + 7$x$ ^{2} ) = 7(1 - $x$ ) + 14($x$ ^{2} + 2)
Solution: 2x + 5 + 2(2 + 7x ^{2} ) = 7(1 - x ) + 14(x ^{2} + 2) [Write the expression.] 2x + 5 + 4 + 14x ^{2} = 7 - 7x + 14x ^{2} + 28 [Distributive property.] 2x + 9 = 35 - 7x [Subtract 14x ^{2} from the two sides of the equation.] 9x + 9 = 35 [Add 7x to both sides of the equation.] 9x = 26 [Subtract 9 from the two sides of the equation.]x = 26 / 9 [Divide throughout by 9.]Correct answer : (1)
10.
The perimeter of a rectangle is represented by $p$ = 2($l$ + $b$ ) where $p$ , $l$ and $b$ are the perimeter, length and width respectively. Solve for $l$ .
Solution: p = 2(l + b )p 2 = l + b [Divide throughout by 2.]p 2 - b = l [Subtract b from the two sides of the equation.]l = p 2 - b Correct answer : (2)