Question

unit 2a: linear expressions & equations day 3: equations, graphs & their solutions
equations, graphs & their solutions
learning target: explain the meaning of solutions to equations in one variable and two - variables. comprehend that the graph of a linear equation represents all solutions to the equation.
activity 4.1: what is a solution? a solution makes a true statement. a granola bite contains 27 calories. most of the calories come from c grams of carbohydrates. the rest come from other ingredients. one gram of carbohydrate contains 4 calories.
the equation 4c + 5 = 27 represents the relationship between these quantities.

1. what could the 5 represent in this situation?
2. priya said that neither 8 nor 3 could be the solution to the equation. explain why she is correct.
3. find the solution to the equation.

Explanation:

Step1: Isolate the term with the variable

We start with the equation $4c + 5=27$. To isolate the term with the variable $c$, we use the subtraction - property of equality. Subtract 5 from both sides of the equation.
$4c+5 - 5=27 - 5$
$4c=22$

Step2: Solve for the variable

Now, to solve for $c$, we use the division - property of equality. Divide both sides of the equation $4c = 22$ by 4.
$c=\frac{22}{4}=\frac{11}{2}=5.5$

Answer:

$c = 5.5$