Solving MultiStep Inequalities Solve for the specified variable

Solving Multi-Step Inequalities

Solve for the specified variable: RA + MB = O; M TI = M ; I FAS = T ; F NE + M = O ; E

Guide to solving for variables:

Guide to solving for variables: Step 1: If there are parenthesis, distribute.

Guide to solving for variables: Step 1: If there are parenthesis, distribute. ◦ 2(X + 5) = 4 X – 4 2*X + 2*5 = 4 X – 4

Guide to solving for variables: Step 1: If there are parenthesis, distribute. ◦ 2(X + 5) = 4 X – 4 2*X + 2*5 = 4 X – 4 ◦ 2*X + 2*5 = 4 X – 4 2 X + 10 = 4 X – 4 Step 2: Simplify multiplication.

Guide to solving for variables: Step 1: If there are parenthesis, distribute. ◦ 2(X + 5) = 4 X – 4 2*X + 2*5 = 4 X – 4 ◦ 2*X + 2*5 = 4 X – 4 2 X + 10 = 4 X – 4 ◦ 2 X + 10 = 4 X – 4 = 2 X + 10 Step 2: Simplify multiplication. Step 3: Get the larger variable on the left. Step 4: Eliminate the variable on the right using addition or subtraction. ◦ 4 X – 4 = 2 X + 10 ◦ -2 x -2 X Step 5: Simplify addition or subtraction. ◦ 2 X – 4 = 10

Guide to solving for variables: Step 6: Eliminate constant on the left using addition or subtraction. ◦ 2 X – 4 = 10 ◦ +4 +4 Step 7: Simplify addition or subtraction. ◦ 2 X = 1 Step 8: Eliminate the coefficient by multiplication or division.

Guide to solving for variables: Step 6: Eliminate constant on the left using addition or subtraction. ◦ 2 X – 4 = 10 ◦ +4 +4 Step 7: Simplify addition or subtraction. ◦ 2 X = 14 Step 8: Eliminate the coefficient by multiplication or division. ◦ 2 X = 14 2 2 X=7

Special case: Fractions:

$Special case: Fractions: ◦ You can eliminate fractions by multiplying EVERYTHING in the equation$

Special case: Fractions: ◦ You can eliminate fractions by multiplying EVERYTHING in the equation by the denominator.

$Special case: Fractions: ◦ You can eliminate fractions by multiplying EVERYTHING in the equation$

Special case: Fractions: ◦ You can eliminate fractions by multiplying EVERYTHING in the equation by the denominator. ◦ ⅓X + 2 = 5 3*⅓X + 3*2 = 3*5 1 X + 6 = 15

Specifics to inequalities:

Specifics to inequalities: Step 3: When you switch sides, flip the inequality. ◦ 2 X + 10 > 4 X – 4 < 2 X + 10

Specifics to inequalities: Step 3: When you switch sides, flip the inequality. ◦ 2 X + 10 > 4 X – 4 < 2 X + 10 Step 8: If you multiply or divide by a negative number, you must flip the inequality.

Specifics to inequalities: Step 3: When you switch sides, flip the inequality. ◦ 2 X + 10 > 4 X – 4 < 2 X + 10 Step 8: If you multiply or divide by a negative number, you must flip the inequality. ◦ -2 X > 10 -2 -2 X < -5