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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 side Every equation has 2 sides, separated by the = sign. 4 + x = 12 right side The solution to an equation is expressed as an equation with the variable ALONE on one side. The solution is : y = 2 example: y + 3 = 5 We also use INVERSE OPERATIONS. The inverse of multiplication is division. The inverse of division is multiplication. The inverse of subtraction is addition. The inverse of addition is subtraction. Example 1 The inverse 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 inverse 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 inverse 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 inverse operations to
undo ADDITION or SUBTRACTION BEFORE undoing MULTIPLICATION or DIVISION.
Use inverse operations to undo the constant before undoing the coefficient. Coefficient 4 x + 9 = 21 Constant Example 1 4 x 4x = 12 4 4 + x - 9 9 = = - 9 21 3 solution divide both sides by 4 subtract 9 from both sides Ask yourself these questions as you solve each equation 1. Can you combine like terms on the LHS? 2. Can you combine like terms on the RHS? 3. What side of the equation is the variable on? 4. Is there a number being added or subtracted to THAT side? (get rid of it!! DO THE OPPOSITE 5. Is there a number next (attached) to the variable? (get rid of it!! DO THE OPPOSITE Example 2 2p - 3 = 27 2p = 30 2 p = 15 + 3 +3 2 add 3 to both sides solution divide both sides by 2 Your turn! 5y - 15 = 20 Fill in the missing numbers. 5y = 35 y = Solve these two step equations. 3y + 8 = 23 3y = 15 y = Solve these two step equations. 4y - 1 = 15 4y = 16 y = Solve these two step equations. 5y - 4 = 36 5y = 40 y = Solve these two step equations. 6y + 7 = 37 6y = 30 y = Solve these two step equations. 8y - 2 = 14 8y = y = Solve these two step equations. 4y + 3 = 51 4y = y = Solve these two step equations. 5y - 1 = 29 5y = y = Solve these two step equations. 3y + 14 = 23 3y = y = Solve these two step equations. 8y - 11 = 21 8y = y = Solve these two step equations. 7y - 9 = 54 y = = Solve these two step equations. 4y + 1 = 33 y = = Solve these two step equations. 2y - 13 = 1 y = = Solve these two step equations. 3y - 8 = 22 y = = Solve these two step equations. 8y - 29 = 3 y = = Solve these two step equations. 9y - 4 = 41 y = = Solve these two step equations. 2y + 7 = 17 y = = Solve these two step equations. 4y - 8 = 32 y = = Solve these two step equations. 5y + 3 = 18 y = = Solve these two step equations. 7y + 9 = 44 y = = 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 Remember: FIRST, undo any addition or subtraction. What you do to one side of the equation, you must do to the other. SHOW your work on both sides! THEN, undo any multiplication. Use inverse operations to isolate the variable. |