Step 1: Begin by adding 2x to both sides 8x + 7 = 5 (to ensure that the terms are together on the same side) x Step 2: Subtract 7 from each side: 8x = -2 Step 3: Divide each side by 8: = -¼ x Solve the following equations, showing each step in your working: Exercise A: 1) 2x + 5 = 19 2) 5x 2 = 13 3) 11 4x = 5 – – 4) 5 7x = -9 5) 11 + 3x = 8 2x 6) 7x + 2 = 4x 5 – – – Example 3: Solve the equation 2(3x 2) = 20 3(x + 2) – – Step 1: Multiply out the brackets: 6x 4 = 20 3x 6 – – – (taking care of the negative signs) Step 2: Simplify the right hand side: 6x 4 = 14 3x – – Step 3: Add 3x to each side: 9x 4 = 14 – Step 4: Add 4: 9x = 18 Step 5: Divide by 9: = 2 x Exercise B: Solve the following equations. 1) 5(2x 4) = 4 2) 4(2 = 3(x 9) x) – – – 3) 8 (x + 3) = 4 4) 14 3(2x + 3) = 2 – – More help: EQUATIONS CONTAINING FRACTIONS When an equation contains a fraction, the first step is usually to multiply through by the denominator of the fraction. This ensures that there are no fractions in the equation. Example 4: Solve the equation Solution: Step 1: Multiply through by 2 (the denominator in the fraction): Step 2: Subtract 10: = 12 y Solve the equation Example 5:
Step 1: Begin by adding 2x to both sides 8x + 7 = 5 (to ensure that the x terms are together on the same side) Step 2: Subtract 7 from each side: 8x = -2 Step 3: Divide each side by 8: x = -¼ Exercise A: Solve the following equations, showing each step in your working: 1) 2x + 5 = 19 2) 5x – 2 = 13 3) 11 – 4x = 5 4) 5 – 7x = -9 5) 11 + 3x = 8 – 2x 6) 7x + 2 = 4x – 5 Example 3: Solve the equation 2(3x – 2) = 20 – 3(x + 2) Step 1: Multiply out the brackets: 6x – 4 = 20 – 3x – 6 (taking care of the negative signs) Step 2: Simplify the right hand side: 6x – 4 = 14 – 3x Step 3: Add 3x to each side: 9x – 4 = 14 Step 4: Add 4: 9x = 18 Step 5: Divide by 9: x = 2 Exercise B: Solve the following equations. 1) 5(2x – 4) = 4 2) 4(2 – x) = 3(x – 9) 3) 8 – (x + 3) = 4 4) 14 – 3(2x + 3) = 2 More help: EQUATIONS CONTAINING FRACTIONS When an equation contains a fraction, the first step is usually to multiply through by the denominator of the fraction. This ensures that there are no fractions in the equation. Example 4: Solve the equation Solution: Step 1: Multiply through by 2 (the denominator in the fraction): Step 2: Subtract 10: y = 12 Example 5: Solve the equation