Practice
1. Is 2 a solution the equation x + 5 = 7? Explain.
2. Is 9 a solution to the equation 5x = 40? Explain.
3. Is 32 a solution to the equation x - 30 = 2? Explain.
4. Is 24 a solution to the equation x = 6? Explain.
4
5. Is 8 a solution to the equation 3x - 5 = 20? Explain.
6. Is 10 a solution to the equation 2x + 11 = 31? Explain.
Different equations may have different numbers of solutions
x=4
1 solution (the equation is only true when x is 4)
4=4
infinitely many solutions (4 is always equal to 4
no matter what the value of x)
4=5
no solution (the statement is false because 4
cannot equal 5)
Practice
State the number of solutions to each equation below (0, 1 or infinitely many)
(a) 2 + x = 5
(b) a = a
(c) 3 = 4
(d) 10 = 10
(e) 3x = 12
(f) x = 7
(g) -2 = 2
(h) n = n
(i) x = -6
3
(j) c = c
(k) 3 = 3
(l) -3 = x
Find the value of x that makes each equation true
(a) 12 + x = 8
(b) x - 20 = 11
(c) -1 = 7 + x
(d) 24 + x = 30
(e) 16 - x = 10
(f) 15 = 30 + x
(g) 46 - x = 25
(h) 14 = -4 + x
(i) 50 = x + -10
(j) -12 = x - 6
(k) 100 + x = 22
(l) 30 = 25 - x
(m) -8 + x = 3
(n) 16 - x = 7
(o) 35 = -10 + x
(p) -20 - x = 10
State the value of x that makes each equation true
(a) 7x + 8 = 36
(b) -4x + 6 = 30
(c) x + 1 = 14
3
(d) -8 + x = -4
2
(g) -3 - 6x = 51
(e) -3x + 7 = -20
(h) x + 8 = 9
3
(f) 26 = 4 - 11x
(i) -38 = 6x - 5
Find the value of x that makes each equation true
x - 7/ 8 = 3/ 4
3
/10 + x = 1/2
0.4x + 3 = 1.2
x - 2/ 9 = 5/ 6
0.25x + 0.6 = -2
4 - 3x/4 = 2/3
10 - 0.3x = 4
6 - 2x/5 = 2
Use the distributive property to expand each expression below
(a) 4(6 - 2x)
(b) 0.5(8x + 4)
(c) -3(3x + 2)
(d) -5(x - 4)
(e) 2(3x + 5)
(f) -2(5x - 1)
Find the value of x that makes each equation true
(a) 3(x - 4) = 18
(b) 50 = 2(5x + 3)
(c) -4(3x + 2) = 20
(d) 1/2(10 - 6x) = 24
(e) 16 = 8(4x + 2)
(f) -7(3x - 1) = 28
(g) 0.25(8x - 16) = -40
(h) -10 = 2(x - 5)
(i) 16 = 2(3 - x)
Find the value of each expression
(a) 5x - 3x
(b) -2d + 8d
(c) 4y - 3y + 7
(e) 4x - 5 + 3x
(f) 10 - 6d + 4
(g) 5x - 2y + 6y
(d) 9x + 6 - 2
(h) 9z + 3w - 10z
Find the value of x that makes each equation true
(a) 4x - 8 + 3x = 20
(b) 32 = 12x - 2(3x + 4)
(c) 10 - 5x + 3 = 27
(d) 100 = 20 - 5(2x + 10)
(e) -7(4x + 2) + 10x = 30
(f) 4x - 3 + 2x - 7 = 15
(g) -20 = 4x - 2(6 - x)
(h) -5x + 3 - 2x = 17
(i) 37 = -2(4 + 4x) - 2x
(j) -4(3x + 6) - 2 = 20
State the value of x that makes each equation true
(a) 4x - 6 = 2x + 8
(b) 12 - 3x = -4 + x
(c) 2(4x - 7) = 10x
(d) 5 - 2x = 13 - 4x
(e) 12 - 5x = -8 - 2x
(f) 12x - 7 = 3(x + 5)
(g) 5(2x + 3) = 6(x - 4)
(h) 5(2x - 1) = 25 + 7x
(i) -8(4 - 2x) = 3(5x - 2)
(j) 10(5x - 6) = 8(4 + 8x)