6.2 Solving Linear Equations Objective: To solve linear equations

Linear equations An equation is made up of two algebraic expressions put together with an = sign. To solve an equation means to find the value of the variable that makes the statement true. For example, x = 2 is a solution to x + 3 = 5 because = 5 is a true statement. Linear equations can be written in the form ax + b = c.

Solving equations by addition and subtraction If a number is being added to the variable subtract it from both sides If a number is being subtracted from the variable add it to both sides

Examples x + 10 = 23 x - 5 = x = 2

Solving equations using multiplication and division If the number is being multiplied times the variable then divide both sides by the number If the number is dividing the variable then multiply both sides by the number. If the variable is being multiplied times a fraction then multiply both sides by the reciprocal of the fraction.

Examples 8k = 36 -7t = 49 c/4 = 16 3/5 x = 15

Solving multi-step equations When solving multi-step equations, reverse addition and subtraction before multiplication and division.

Examples: Solve 1. 4a – 5 = 15

Solving equations with variables on both sides 1.6k-3=2k t+7=3t-5 3.3n+1=7n-5

More examples: first use the distributive property 1.2(x – 4) + 5x = – 2(t + 1) = -3t (k+4)=5(k – 3) x – 5(2 + x) = 2(x + 1)

Equations with fractions To solve equations with fractions first multiply both sides by the least common denominator of all denominators on both sides.

Examples: Equations with fractions

Solving for a specific variable Solve T = D + pm for m Solve I = Prt for P Solve 3x + 6y = 12 for y

HW: p.289/1-73