Equation Architect Worksheet Equation Architect
TEKS A.5.A
Name:
Date:
Phase 1: The Blueprint
Solve the equation step-by-step: 3(x - 4) = 2x + 5
1
Distribute the 3:
3x -
= 2x + 5
2
Move variables to one side:
- 12 = 5
3
Final Step:
x =
Phase 2: Guided Construction
Tip: Distribute first, then combine like terms.
4(x + 2) = 2(x - 6)
Tip: Clear the fraction by multiplying by 2.
\[ \frac{1}{2}(4x - 8) = 10 \]
Phase 3: Structural Integrity
1. What is the solution to \( 5(x - 3) = 2x + 6 \)?
A 7
B 3
C 9
D -3
2. Solve for n: \( 2n + 15 = 5(n - 3) \)
F 10
G 0
H -10
J 5
3. Which value of x satisfies \( 0.5(x + 4) = 3x - 8 \)?
A 4
B 2
C 8
D 10
4. Solve: \( 4(2x - 1) = 6x + 10 \)
F 7
G -7
H 3
J 11
5. What is the value of x in \( 12 - 3x = 2(x + 1) \)?
A 2
B 5
C -2
D 10
6. Solve for n: \( \frac{2}{3}(n + 6) = 10 \)
F 9
G 15
H 21
J -9
7. Solve: \( -2(x - 5) = 4x - 8 \)
A 3
B 1
C -3
D 0
8. Which value of x makes \( 8x - 2 = 5x + 13 \) true?
F 5
G 3
H 11
J -5
9. Solve for x: \( 0.25(4x + 8) = x + 2 \)
A x = 0
B All real numbers
C No solution
D x = 2
10. What is the solution to \( 7x - (2x + 3) = 12 \)?
F 3
G -3
H 1.8
J 5
Inequality Investigator Worksheet Inequality Investigator
TEKS A.5.B
Name:
Date:
Phase 1: The Golden Rule
Critical Evidence:
When you multiply or divide by a negative number, you MUST flip the inequality sign!
Solve: -4(x - 2) ≥ 12
1
Distribute the -4:
-4x +
≥ 12
2
Subtract 8 from both sides:
-4x ≥
3
Divide by -4 (FLIP THE SIGN!):
x
≤
Phase 2: Gathering Evidence
Case #101: 3(2x - 5) < 9
Case #102: 2x + 10 ≤ 5x - 8
Phase 3: The Verdict
1. Which inequality represents the solution to \( 4(x - 3) > 10x + 6 \)?
A x < -3
B x > -3
C x < 3
D x > 3
2. Solve the inequality: \( -2n + 15 \le 5 \)
F n ≤ 5
G n ≥ 5
H n ≤ -5
J n ≥ -5
3. A taxi charges $5.00 plus $2.00 per mile. If a passenger has no more than $25.00, which describes m, the number of miles?
A m ≤ 10
B m ≥ 10
C m < 15
D m ≤ 15
4. Solve: \( \frac{x}{-3} + 5 < 2 \)
F x < 9
G x > 9
H x < -9
J x > -9
5. What is the solution to \( 3(x + 1) - 2x \ge 5 \)?
A x ≥ 2
B x ≤ 2
C x ≥ 8
D x ≤ 8
6. Solve for y: \( 10 - 2y \ge 4 \)
F y ≤ 3
G y ≥ 3
H y ≤ 7
J y ≥ 7
7. Which set of numbers makes \( 2x - 3 > 7 \) true?
A {4, 5, 6}
B {6, 7, 8}
C {3, 4, 5}
D {5, 6, 7}
8. Solve: \( 5(x - 2) \le 3(x + 4) \)
F x ≤ 11
G x ≤ 1
H x ≥ 11
J x ≥ 1
9. What is the solution to \( -(x - 5) > 10 \)?
A x < -5
B x > -5
C x < 15
D x > 15
10. Solve: \( 4 - x > 2x + 10 \)
F x < -2
G x > -2
H x < 2
J x > 2
Slope Scout Worksheet Slope Scout
TEKS A.3.B
Name:
Date:
Phase 1: The Trail Map
From a Table:
\[ m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \]
From a Graph:
m = \frac{\text{rise}}{\text{run}}
Phase 2: Field Practice
Table Scout:
Rise (\(\Delta y\)): ___ Run (\(\Delta x\)): ___
Graph Scout:
m = rise/run = ____
Phase 3: Navigation Mastery
1. What is the rate of change of the amount earned with respect to hours worked?
A $15/hr
B $30/hr
2. What is the rate of change for the function graphed below?
F 1
G -1
3. Which equation has a rate of change of -3?
A y = 3x
B y = -3x
C y = 1/3x
D y = -1/3x
4. Calculate the slope: (2, 5) and (4, 13).
F 4
G 2
H 8
J 1/4
5. A line passes through (0, 4) and (2, 0). What is the slope?
A -2
B 2
C -1/2
D 1/2
6. Slope from table: (1, 3), (2, 6), (3, 9)
F 3
G 1/3
H 1
J 6
7. Find the rate of change for \( y = 2/3x + 4 \).
A 2/3
B 3/2
C 4
D 0
8. Rate of change from (5, 10) and (10, 15)?
F 1
G 5
H 2
J 10
9. Graph passes through (0,0) and (1,5). Rate of change?
A 5
B 1/5
C 1
D 0
10. Find slope: \( 3x - y = 5 \)
F 3
G -3
H 1/3
J -5
Linear Mastery Mini Checks Worksheet Mastery Slip #1 (A.5.A)
Equation Architect Check
Name: __________________________
STAAR LEVEL
1. What is the solution to the equation below?
3(2x - 4) = 4x + 10
A x = 11
B x = 7
C x = 1
D x = 22
Mastery Slip #2 (A.5.B)
Inequality Investigator Check
Name: __________________________
STAAR LEVEL
1. Which inequality represents the solution to \( -3x + 15 < 3 \)?
F x < 4
G x > 4
H x < -4
J x > -4
Mastery Slip #3 (A.3.B)
Slope Scout Check
Name: __________________________
STAAR LEVEL
1. What is the rate of change for the linear function shown in the table?
A 3
B 1/3
C 6
D 2
