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8.1 Solve Equations that Contain Addition and Subtraction Common Core Standards 8. EE.7. Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. WARM-UP Fill in the blank. 1) _____ + 3 = 7 2) 19 = ____ + 10 3) _____ − 8 = 1 4) 10 = ____ − 6 Find x. 5) x + 7 = 12 6) x − 1 = 14 Solve Equations that Contain Addition and Subtraction How do we figure out the missing number when we can't do the problem in our head? 476 = x + 318 1.6 = x − 2.37 NOTES Addition and subtraction are called inverse operations because they undo each other. Concept Check Evaluate the expressions. 13 + 5 − 5 Simplify the expression. x+4−4 17 − 2 + 2 NOTES The Properties of Equality – Any operation done to one side of an equation must be repeated exactly on the other side for the equation to remain true. Concept Check Are the equations true? 4 + 7 = 11 4 + 7 − 7 = 11 − 7 4 + 7 = 11 − 7 NOTES To solve one-step equations perform the inverse operation to both sides to get x by itself. Examples Solve the equation. x + 15 = 37 x − 9 = 43 17 = x + 8 38 = x − 18 NOTES The answer to an equation is called the solution. Examples Find the solution. x + 3.2 = 7.9 18.7 = x + 5 x − .8 = 4.7 EXAMPLES If the perimeter is 24.5 inches, write and solve an equation to find its missing length. 8 in 8in x PRACTICE Solve the equations. x − 68 = 159 43.7 = x + 6.5 24.4 = x − 3 17 = x + 1.3 PRACTICE Find the missing length if the perimeter is 30 centimeters. 5 cm x 12 cm FINAL QUESTION Find the solution. x − 136 = 18.1