# Solving Equations

 You will get asked to solve equations in your exam.  Below are the types of equations you should study if your aiming for a C in maths.  Equations can crop up on either your calculator or non calculator paper but they will probably turn up on both!

Example Question

 Solve: a) 3(2x - 4) = 18 b) 2x + 14 = 2(2x - 3)

Solution

 a) To solve equations we want to find the value of x.  In other words we want x on its own the left hand side of the equation.  To achieve this we need to use inverse operations. 3(2x - 4) = 18 First expand the brackets to get: 6x - 12 = 18 Now to get rid of "-12" we add 12 to both sides which gives: 6x = 30 Finally remember "6x" means "6 times by x" so we divide both sides by 6: x = 30 ÷ 6 x = 5 b) Here we have a slightly harder example but the basic method stays the same. 2x + 14 = 2(2x - 3) First expand the brackets to get: 2x + 14 = 4x - 6 Now since we have x terms on both sides of the equation we write the equation with the larger x term on the left: 4x - 6 = 2x + 14 Now we get rid of the smaller 2x term by subtracting 2x from both sides: 2x - 6 = 14 Now add 6 to both sides: 2x = 20 Finally divide both sides by 2 gives: x = 10

Test Yourself!
 Grade G/F Solve:     a + 2 = 10 a = G/F Solve:     3b = 45 b = E/D Solve:     2c - 4 = 18 c = D Solve:     4(d + 2) = 10 d = D/C Solve:     5(e - 2) = 3e e = D/C Solve:     5f - 1 = 6 + 3f f = C Solve:     7(g - 2) = 2(2g + 5) g = C Solve:     5(h + 2) = 12 + h h =