solve for x equations
This year, a salesman sells a total of $60,000 worth of steak knives by going door-to-door. This represents a 20% increase from the year before. What was the value of his sales last year?
A. $45,000
B. $48,000
C. $50,000
D. $52,500
E. $56,000
Let x represent the total value of last year’s sales, Set up an equation and solve it for x. Since the salesman’s sales increased by 20% since last year’s, his current sales 120% of x, or 1.2x. So,
1.2x = 60,000
Solve the equation for x by dividing both sides by 1.2.
x = 50,000
Therefore, the salesman sold $50,000 worth of steak knives last year.
(a) 4a + 6a
(a) 4a + 6a = 10a
(a) 3x . 2x
(a) 3x . 2x = 6x2
32a / 8b
4ab
(3n + 2)(n + 3)
3n2 + 11n + 6
Solve the equation for x.
x/3 = (2x + 3)/7
A. –3
B. 2
C. 3
D. 3/7
E. 9
This equation is a proportion, so it can be solved by cross-multiplication. Form a new equation by multiplying the numerator of each fraction by the denominator of the fraction on the other side. Then, simplify the result and solve for x.
x/3 = (2x + 3)/7
7x = 3(2x + 3)
7x = 6x + 9
x = 9
(b) 12pq − 6pq + 4pq
(b) 12pq − 6pq + 4pq = 10pq
(b) 4p . -2q
(b) 4p . -2q = -8pq
24a / 6
4a
(n − 1)(2n − 2)
2n2 − 4n + 2
Solve the equation for y.
3(2y + 4) = 8y
A. –8
B. –6
C. –2
D. 2
E. 6
To begin, simplify the right side of the equation by distributing the 3.
3(2y + 4) = 8y
6y + 12 = 8y
Then, solve the equation by isolating the variable and dividing both sides by the coefficient.
12 = 2y
y = 6
(c) 3c + 4d + 5c
(c) 3c + 4d + 5c = 3c + 5c + 4d
= 8c + 4d
4w . 8z
32wz
12x / 4
3x
(2x + 3)(2x − 3)
4x2 − 9
Solve the equation for x.
|x + 5| = 3
A. -8
B. -3
C. -2
D. -8 and -3
E. -8 and -2
This equation involves an absolute value function. The absolute value of a number is its distance from zero on a number line. Since distances are never negative, the absolute value of a number is always positive (or equal to zero). In order to make the equation true, the expression inside the absolute value, x + 5, can equal either -3 or 3 since the absolute value of both values is 3. Write two equations and solve each.
x + 5 = -3
x = -8
x + 5 = 3
x = -2
(d) 2x2 + x + 5x2 − 3x
(d) 2x2 + x + 5x2 − 3x
= 2x2 + 5x2 + x − 3x
= 7x2 − 2x
7p . -2c
-14pc
18a / 2
9a
(2n + 3)(2n + 1)
4n2 + 8n + 3
If 3x + 8x + 4x = 6x + 63, then what is 5x + 23?
A. 28
B. 35
C. 38
D. 58
E. 62
To begin, solve the given equation for x.
3x + 8x + 4x = 6x + 63
15x = 6x + 63
9x = 63
x = 7
Next, substitute 7 for x in the expression 5x + 23 and simplify the result.
5(7) + 23 = 35 + 23 = 58
(a) 8a+6a
(a) 8a+6a=14a
12b . 2a
24ba
22x / 2t
11xt
(3p − 3)( p − 1)
3p2 − 6p + 3