Students must be able to write equations that contain only one-variable which will appear on both sides of the equation. The coefficient for the variable could be a fraction or decimal. When substituted back into the equation, the solution to the equation, which is the variable, will make the equation true or both sides equal to each other. Students must also write inequalities that contain one-variable which will appear on both sides of the inequality. Students should understand combining like terms and the distributive property to write one-variable equations and inequalities.

Read the following problem situations, solve, and justify your thinking.

 

Mrs. Lowe charges $45 an hour with a $10 flat fee for tutoring. Mrs. Smith charges $40 an hour with a flat fee of $15 to tutor. Write an equation that represents the situation when the cost is the same to be tutored by Mrs. Lowe and Mrs. Smith. Taxi A charges $0.25 per mile and an initial fee of $5. Taxi B charges $0.5 per mile and an initial fee of $2. Write an inequality that can be used to determine when the cost of Taxi B will be greater than Taxi A. 

 

8.8 Expressions, equations, and relationships. The student applies mathematical process standards to use one-variable equations or inequalities in problem situations. The student is expected to:

(A) write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants