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It is important to learn this process, so that you can apply it to more difficult equations! Solving Two-Step Equations left hand side Every equation has 2 sides, separated by the = sign. 4 + x = 12 right hand side The opposite of multiplication is division. The opposite of division is multiplication. The opposite of subtraction is addition. The opposite of addition is subtraction. We also use OPPOSITE OPERATIONS to get the pro-numeral by itself. Example 1 The opposite of addition is subtraction, so we need to subtract 9 from both sides of the equation. We need to UNDO the 9, which is added to p. p + 9 = 12 p - 9 = - 9 3 You must show the steps of solving your equations in this manner! Example 2 We need to UNDO the 3, which is subtracted from s. The opposite of subtraction is addition, so we need to add 3 to both sides of the equation. s s - 3 = 17 + 3 = + 3 20 You must show the steps of solving your equations! Example 3 The opposite of multiplication is division, so we need to divide both sides of the equation by 5. We need to UNDO the 5, which is multiplied by x. ÷ 5x = 35 x 5 = ÷ 5 7 You must show the steps of solving your equations! We use this same process when more than one number is on the same side of the equation as the variable. However, it is important to remember to use opposite operations to
undo ADDITION or SUBTRACTION BEFORE undoing MULTIPLICATION or DIVISION.
(Remove the seperate value first) Example 1 4 x ÷4 ÷4 4x = 12 + x - 9 9 = = - 9 21 3 solution divide both sides by 4 subtract 9 from both sides Example 2 2p - 3 = 27 2p = 30 ÷2 p = 15 + 3 +3 ÷2 add 3 to both sides solution divide both sides by 2 What is the first step in solving this equation? 6a - 3 = 21 add 6 add 3 subtract 6 subtract 3 Identify the next step in solving this equation. 4b + 8 = 56 4b + 0 = 48 4b = 48 - 8 add 4 to both sides multiply both sides by 4 divide both sides by 4 subtract 4 from both sides -8 Your turn! 5y - 15 = 20 Fill in the missing numbers. ÷ 5y = 35 y = ÷ Solve. 3y + 8 = 23 ÷ 3y = 15 y = ÷ Solve. 6y + 7 = 37 ÷ 6y = 30 y = ÷ Solve. 8y - 2 = 14 ÷ 8y = y = ÷ Solve. 4y + 3 = 51 ÷ 4y = y = ÷ Solve. 7y - 9 = 54 ÷ y = = ÷ Solve. 4y + 1 = 33 ÷ y = = ÷ |