Download Absolute Value Equations

Chapter 1 Review
Evaluating Expressions
• Properties of Real Numbers
• Solving Equations
• Solving Inequalities
•
Evaluate Expressions
Follow the order of operations. Be careful of
exponents, brackets and absolute values.
Evaluate if h = -8, x = 4, y = -2, and z = 3.5
1) z – x + y²
2) x + 6 [ 8(y + z) – x]
3) -|h + 12|
4) |4x + 3| - 12
Real Numbers (R)
Rational (Q)
Integers (Z)
Whole (W)
Natural (N)
Irrational(I)
Solve Equations
Algebra Equations
-Eliminate Parentheses
-Combine like terms
Absolute Value Equations
-Isolate the absolute value, if a negative distance
then no solution is the answer.
-Write two equations
One to the positive distance
Other to the negative distance
-Solve each equation
-Check solutions
Solve the following equations
1. ⅓y = -2
2. -10x + 3(4x – 2) = 6
3. -¾n + 1 = -11
4. 8 – 5y = y + 2
5. 3 = |2x + 7|
6. -9 = -3|2n + 5|
7. -1 = |c -2| - 5
8. |h – 5| = 7
Solve for a variable
3. 5x – 2y = z.
a) Solve for x.
b) Solve for y
4. d = g + gpt
a) Solve for t
b) Solve for g
Solve Inequalities
Multiply/Divide by an negative number then
change the inequality!
Singular inequality
Elimination Parentheses
Combine like terms
Graph answer on number line
Compound inequality
Solve each inequality
Graph each on one number line
Shade and- overlapping
or- each arrow
Solve Inequalities
Absolute Value Inequalities
Isolate the absolute Value
Determine if “and” / “or” statement
Write two inequalities
-One with given inequality and distance
-Other with opposite inequality and distance
Solve each inequality
Graph each inequality on one number line
Shade and- overlap
or- each arrow
Solve and graph on a number line.
1) a + 2 > 3.5
2) 25 – 3x > 2 – 3x
3) 5 ≤ 2w + 19
4) n > (n – 4)/5
Examples. Solve and graph on a number line.
1)10 ≤ 3y – 2 < 19
2) -4 < 3x – 1 < 14
3) x + 3 < 2 or -x ≤ -4
4) y + 5 ≤ 7 or y - 6 > 2
Solve and graph the solution set on a number line.
1) |4k| < 20
2) |3x + 4|≥ 10
3) |7X| + 4 < 0
4) (|N - 3|) /2 > 8
Write an inequality. Then solve.
1. The product of 6 and a number is less than 24.
2. The sum of a number and -2 is more than 14.
3. Four less than double a number is at most eight.
Write and inequality for each problem. Then solve.
1) Sophia’s goal is to score at least 200 point this
basketball season. If she has already scored 122
points, how many points does Sophia have to score
on average for the last 6 games to reach her goal?
2) Allen has at most $15.00 to spend today. He buys
a bag of potato chips and a can of soda for $1.59. If
gasoline at this store costs $2.89 per gallon, how
many gallons of gasoline, to the nearest tenth of a
gallon, can Allen buy for his car?