1. Solving Equations: More Than One Step The algebra tiles show the equation 2x –3 = 5 = When you solve equations, the object is to get the variable alone, or to ISOLATE THE VARIABLE, on one side of the equal sign. Example 1-Solution 4x + 3 =11 4x + 3 = 11Subtract 3 from both sides:4x + 3 –3 = 11 –3 4x = 8 Divide both sides by 4: 4x 4 = 8 4 x = 2 To check the answer, put 2 back into the first equation.

2. Solving Equations: More Than One Step Example 2Solution3(x-1) = x + 5 3(x-1) = x + 5Remove brackets3x –3 = x + 5 Subtract x from both sides:3x –x – 3 = x –x + 5 2x –3 = 5 Add 3 to both sides:2x –3 + 3 = 5 + 3 2x = 8 Divide both sides by 2:2x 2 = 8 2 x = 4 To check the answer, put 4 back into the first equation.

3. Solving Equations: More Than One Step 1.2x + 1 = 5 2.4b + 2 = 6 + 4 3.3y – 5 = -2 4.4z – 7 = 3 + 10 5.M/5 –2 = -1 6.3x + 2x = 15 7.2z + 4 = 5z – 8 8.5(y-3) = y + 1 9.5(g-3) + 2 = 3(g+1) 10.-3(1-b) = 2(b+1)

4. Equations with Rational Solutions The algebra tiles show the equation x – 2 = -7 = Equations can have negative numbers as solutions. These equations are solved the same way. Example 1Solution x + 5 = 3 x + 5 = 3 Subtract 5 from both sides: x + 5 – 5 = 3 – 5 x = -2 The solution is x = -2

5. Equations with Rational Solutions Example 2Solution 2x – 3 = -8 Add 3 to both sides:2x – 3 + 3 = -8 + 3 2x = -5 Divide both sides by 2: 2x 2 = -5 2 x = -2.5

6. Equations with Rational Solutions Example 3Solution4(y-1) + 3 = 2y –7 Expand:4y – 4 + 3 = 2y –7 4y – 1 = 2y – 7 Add 1 to both sides: 4y – 1 + 1 = 2y – 7 + 1 4y = 2y – 6 Subtract 2y from both sides: 4y – 2y = 2y – 2y – 6 2y = -6 Divide both sides by 2: 2y 2 = -6 2 y = -3 The solution is y = -3

7. Equations with Rational Solutions 1.2(x-1) + 7 = 4x + 3 2.5x – 8x = 3(x + 4) 3.5t – 3t = 5 – 3(t-5) 4.m – (-2.2) = 5.4 5.5w/3 = -4 6.n/4 + 3/2 = 5/2