Unit 4. Day 13.

A math “sentence” with an equal sign Q: What is an equation? A: A math “sentence” with an equal sign 3𝑥 + 4 = 78 3 5−𝑦 =6−3𝑦 6 𝑎+5 =7−9𝑎 Q: What does it mean to solve an equation? A: To find the value of the variable Q: How do we solve an equation? A: Isolate the variable

5 4 𝑥 = 𝑥− 3 4 = 1 2 = = Example A: Solve. + 3 4 + 3 4 1 2 + 3 4 𝑥− 3 4 = 1 2 + 3 4 + 3 4 5 4 𝑥 = 1 2 + 3 4 2 4 + 3 4 5 4 = =

𝑚− 2 7 =4 Example B*: 𝑦+ 5 6 = 3 4 Example C*:

30 7 𝑚 = 𝑚− 2 7 =4 = = = Example B*: Solve. + 2 7 + 2 7 4+ 2 7 𝑚− 2 7 =4 + 2 7 + 2 7 30 7 𝑚 = 4+ 2 7 4 1 + 2 7 28 7 + 2 7 30 7 = = =

− 1 12 𝑦 = 𝑦+ 5 6 = 3 4 = = Example C*: Solve. − 5 6 − 5 6 3 4 − 5 6 𝑦+ 5 6 = 3 4 − 5 6 − 5 6 − 1 12 𝑦 = 3 4 − 5 6 9 12 − 10 12 − 1 12 = =

3 8 𝑥 = 1 10 1 10 ∙ 𝑥 = ÷ 3 8 𝑥 = 1 10 ∙ 𝑥 = ∙ 𝑥 = = = Example D: 3 8 3 8 𝑥 = 1 10 1 10 ∙ 𝑥 = ÷ 3 8 3 8 3 8 8 3 3 8 𝑥 = 1 10 8 3 ∙ 𝑥 = ∙ 8 30 4 15 1 10 8 3 8 30 𝑥 = ∙ = =

6 5 ℎ = 3 4 Example E*: − 3 2 𝑥+ 1 6 = 7 8 Example F*:

6 5 ℎ = 3 4 3 4 ∙ ℎ = ÷ 6 5 ℎ = 3 4 ∙ ℎ = ∙ ℎ = = = Example E*: 6 5 6 5 ℎ = 3 4 3 4 ∙ ℎ = ÷ 6 5 6 5 6 5 6 5 ℎ = 3 4 5 6 5 6 ∙ ℎ = ∙ 15 24 5 8 3 4 5 6 15 24 ℎ = ∙ = =

− 3 2 𝑥+ 1 6 = 7 8 = = − 3 2 𝑥 17 24 = 𝑥= Example F*: Solve. − 1 6 − 3 2 𝑥+ 1 6 = 7 8 Example F*: Solve. 7 8 − 1 6 21 24 − 4 24 17 24 − 1 6 − 1 6 = = − 3 2 𝑥 17 24 ∙ = − 3 2 − 3 2 17 24 − 3 2 𝑥= ÷ 17 24 − 2 3 34 2∙17 − 17 36 𝑥 = ∙ = − = = 72 2∙2∙2∙3∙3