WORKSHEET: Algebraic Proof
Name: ____________________
13.Jul.17
1. GIVEN: 4x = 12x + 32 Prove: x = -4
2. GIVEN: 28 + 12x = 8x – 4
Prove: x= -8
3. GIVEN: 60x + 153 = 9x + 51 Prove: x = -2
4. GIVEN: -4x + 10 = -5x + 18
Prove: x= 8
5. GIVEN: -3(x + 2) = 16 – x Prove: x = -11
6. GIVEN: -x – 2(9 – 8x) = 12
Prove: x = 2
WORKSHEET: Algebraic Proof
Name: ____________________
13.Jul.17
I.
4x = 12x + 32 Prove: x = -4
STATEMENTS
1. 4x = 12x + 32
2. -12x + 4x = -12x + 12x + 32
3. -8x = -12x + 12x + 32
4. -8x = 0 + 32
5. -8x = 32
REASONS
1. Given
2. Add. Prop. =
3. Substitution
4. Add. Inverse Prop.
5. Add. Identity Prop.
6.
6. Div. Prop. =
-8x 32
=
-8 -8
32
7. 1x =
-8
32
8. x =
-8
9. x = -4
II.
GIVEN: 28 + 12x = 8x – 4
STATEMENTS
1. 28 + 12x = 8x – 4
2. -28 + 28 + 12x = -28 + 8x – 4
3. 0 + 12x = -28 + 8x – 4
4. 12x = -28 + 8x – 4
5. 12x = 8x + -28 – 4
6. 12x = 8x + -32
7. -8x + 12x = -8x + 8x – 32
8. 4x = -8x + 8x + -32
9. 4x = 0 + -32
10. 4x = -32
4x -32
=
4
4
-32
12. 1x =
4
-32
13. x =
4
11.
14. x = -8
7. Mult. Inverse Prop.
8. Mult. Identity Prop.
9. Substitution
\QED
Prove: x= -8
REASONS
1. Given
2. Add. Prop. =
3. Add. Inverse Prop.
4. Add. Identity Prop.
5. CPA
6. Substitution
7. Add. Prop. =.
8. Substitution
9. Add. Inverse Prop.
10. Add. Identity Prop.
11. Div. Prop. =
12. Mult. Inverse Prop.
13. Mult. Identity Prop.
14. Substitution
\QED
WORKSHEET: Algebraic Proof
Name: ____________________
13.Jul.17
III.
GIVEN: 60x + 153 = 9x + 51 Prove: x = -2
STATEMENTS
1. 60x + 153 = 9x + 51
2. -9x + 60x + 153 = -9x + 9x + 51
3. -9x + 60x + 153 = 0 + 51
4. -9x + 60x + 153 = 51
5. 51x + 153 = 51
6. 51x + 153 – 153 = 51 – 153
7. 51x + 0 = 51 – 153
8. 51x = 51 – 153
9. 51x = -102
1. Given
2. Add. Prop. =
3. Add. Inverse Prop.
4. Add. Identity Prop.
5. Substitution
6. Subtraction Prop. =
7. Add. Inverse Prop.
8. Add. Identity Prop.
9. Substitution
10.
10. Div. Prop. =
51x -102
=
51
51
-102
11. 1x =
51
-102
12. x =
51
13. x = -2
IV.
GIVEN: -4x + 10 = -5x + 18
STATEMENTS
1. -4x + 10 = -5x + 18
2. 5x + -4x + 10 = 5x + -5x + 18
3. 5x + -4x + 10 = 0 + 18
4. 5x + -4x + 10 = 18
5. x + 10 = 18
6. x + 10 – 10 = 18 – 10
7. x + 0 = 18 – 10
8. x = 18 – 10
9. x = 8
REASONS
11. Mult. Inverse Prop.
12. Mult. Identity Prop.
13. Substitution
\QED
Prove: x= 8
REASONS
1. Given
2. Add. Prop. =
3. Add. Inverse Prop.
4. Add. Identity Prop.
5. Substitution
6. Subtraction Prop. =
7. Add. Inverse Prop.
8. Add. Identity Prop.
9. Substitution
\QED
WORKSHEET: Algebraic Proof
Name: ____________________
13.Jul.17
V.
GIVEN: -3(x + 2) = 16 – x Prove: x = -11
STATEMENTS
1. -3(x + 2) = 16 – x
2. -3x + -6 = 16 – x
3. 3x + -3x + -6 = 3x + 16 – x
4. 0 + -6 = 3x + 16 – x
5. -6 = 3x + 16 – x
6. -6 = 16 + 3x – x
7. -6 = 16 + 2x
8. -16 + -6 = -16 + 16 + 2x
9. -16 + -6 = 0 + 2x
10. -16 + -6 = 2x
11. -22 = 2x
1. Given
2. Distributive Prop.
3. Add. Prop. =
4. Add. Inverse Prop.
5. Add. Identity Prop.
6. CPA
7. Substitution
8. Add. Prop. =.
9. Add. Inverse Prop.
10. Add. Identity Prop
11. Substitution
10.
12. Div. Prop. =
-22 2x
=
2
2
-22
11.
= 1x
2
-22
12.
=x
2
13. -11 = x
14. x = -11
VI.
GIVEN: -x – 2(9 – 8x) = 12
STATEMENTS
1. -x – 2(9 – 8x) = 12
2. -x – 18 + 16x = 12
3. –x + 16x – 18 = 12
4. 15x – 18 = 12
5. 15x – 18 + 18 = 12 + 18
6. 15x + 0 = 12 + 18
7. 15x = 12 + 18
8. 15x = 30
15x 30
=
15 15
30
11. 1x =
15
30
12. x =
15
9.
13. x = 2
REASONS
13. Mult. Inverse Prop.
14. Mult. Identity Prop.
15. Substitution
16. Symmetric Prop =
\QED
Prove: x = 2
REASONS
1. Given
2. Distributive Prop.
3. CPA
4. Substitution
5. Add. Prop. =
6. Add. Inverse Prop.
7. Add. Identity Prop.
8. Substitution
10. Div. Prop. =
11. Mult. Inverse Prop.
12. Mult. Identity Prop.
13. Substitution
\QED