Chapter 6 - Algebra: Equations and Inequalities - 6.2 Linear Equations in One Variable and Proportions - Exercise Set 6.2 - Page 362: 30

{6}

8x + 1 = x + 43 Step 1 : Collect variable terms on one side and constants on the other side. subtract x from both the sides 8x + 1 - x = x + 43 -x Simplify 7x + 1 = 43 Subtract 1 from both the sides 7x +1 -1 = 43 -1 Simplify 7x = 42 Divide both the sides by 7 $\frac{7x}{7}$ = $\frac{42}{7}$ x =6 Now we check the proposed solution,6 , by replacing x with 6 in the original equation. Step 1: the original equation 8x + 1 = x + 43 Step2: Substitute 6 for x 8(6) + 1 = 6 + 43 Step 3: Multiply 8.6 = 48 48 + 1 = 6 + 43 Step 4: Solve 49 = 49 Since the check results in true statement, we conclude that the solution set of the given equation is {6}