algebra 1

solve for x equations

100

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.

200

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

300

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

400

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

500

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

simplifying expressions (addition)

100

(a) 4a + 6a

(a) 4a + 6a = 10a

200

(b) 12pq − 6pq + 4pq

(b) 12pq − 6pq + 4pq = 10pq

300

(c) 3c + 4d + 5c

(c) 3c + 4d + 5c = 3c + 5c + 4d

= 8c + 4d

400

(d) 2x2 + x + 5x2 − 3x

(d) 2x2 + x + 5x2 − 3x
= 2x2 + 5x2 + x − 3x
= 7x2 − 2x

500

(a) 8a+6a

(a) 8a+6a=14a

simplifying expressions (multiplication)

100

(a) 3x . 2x

(a) 3x . 2x = 6x2

200

(b) 4p . -2q

(b) 4p . -2q = -8pq

300

4w . 8z

32wz

400

7p . -2c

-14pc

500

12b . 2a

24ba

simplifying expressions (division)

100

32a / 8b

4ab

200

24a / 6

4a

300

12x / 4

3x

400

18a / 2

9a

500

22x / 2t

11xt

Multiplying Binomials

100

(3n + 2)(n + 3)

3n² + 11n + 6

200

(n − 1)(2n − 2)

2n² − 4n + 2

300

(2x + 3)(2x − 3)

4x² − 9

400

(2n + 3)(2n + 1)

4n² + 8n + 3

500

(3p − 3)( p − 1)

3p² − 6p + 3