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1. Write a math problem in which two numbers add together to equal ten. 2. Do the same problem as above except make one of the numbers negative. 3. Do #1 except have one of the numbers be a square root . 4. Do #1 except have one of the numbers be a square root , and the other be a negative number. You plan to go hiking in the Grand Canyon. You estimate you’ll hike at a rate of 2 miles per hour on a steep trail. How long will it take you to hike a 36 mile stretch of marble canyon? Time = 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒓𝒂𝒕𝒆 Time = 𝒕 (hours) Distance = 𝟑𝟔 (miles) Rate = 𝟐 (mph) 𝟑𝟔 𝒕= 𝟐 𝟏𝟖 𝐇𝐨𝐮𝐫𝐬 Negative Numbers −𝟓 + 𝟑 = -5 -4 -3 -2 -1 −𝟐 0 1 2 3 4 5 Negative Numbers −𝟏 + −𝟑 = −𝟒 -5 -4 -3 -2 -1 0 1 2 3 4 5 Negative Numbers −𝟏𝟒 + 𝟐𝟖 = 1𝟒 −𝟐𝟑 + −𝟕 = −𝟑𝟎 1𝟓 − −𝟕 = 𝟐𝟐 What is a Variable? X Y A variable is a letter or a symbol that stands for a number. Variable Substitution Solve when 𝑥 = −2 3x = 𝟑 −𝟐 = −𝟔 1st – Substitute a number for each variable. Use parentheses!!!!!!!!!!!!! Examples 1. Solve for T = 3. 3T + 5 3(3) + 5 9+5 14 2. Solve for 𝒋 = −𝟐. −𝟒𝐣 − 𝟑 −𝟒 −𝟐 − 𝟑 𝟖−𝟑 5 Examples Solve for g = 2 and s = 4 1g + 1s 4 5 1(2) + 1(4) 4 5 1+4 2 5 5+8 10 10 3 1 10 Examples 1. Evaluate for n = 7. n + 5 + (n + 3) 7 + 5+ (7 + 3) 7 + 5+(10) 12+ 10 22 2. Evaluate for 𝒃 = −𝟑. 𝒃 − 𝟖 + (𝒃 + 𝒃) −𝟑 − 𝟖 + (−𝟑 − 𝟑) −𝟏𝟏 − 𝟔 −𝟏𝟕 Closing • What does the word variable mean? • What does the word substitute mean? • How do we substitute for a variable?