To solve the given expressions, we will substitute the values from the table into each expression and simplify step by step. Let's go through each expression one by one.
Table of Values:
- \( a = 3 \)
- \( b = 5 \)
- \( c = 8 \)
- \( m = 10 \)
- \( n = 14 \)
- \( t = 20 \)
- \( u = 25 \)
- \( x = -2 \)
- \( y = -5 \)
- \( z = 0.5 \)
---
Expression 1: \( 3(4 + 9x) \)
Substitute \( x = -2 \):
\[
3(4 + 9(-2)) = 3(4 - 18) = 3(-14) = -42
\]
Answer: \(-42\)
---
Expression 2: \(-3(2n + 3)\)
Substitute \( n = 14 \):
\[
-3(2(14) + 3) = -3(28 + 3) = -3(31) = -93
\]
Answer: \(-93\)
---
Expression 3: \(-2(4 + 3t)\)
Substitute \( t = 20 \):
\[
-2(4 + 3(20)) = -2(4 + 60) = -2(64) = -128
\]
Answer: \(-128\)
---
Expression 4: \(-2(-4m - 8)\)
Substitute \( m = 10 \):
\[
-2(-4(10) - 8) = -2(-40 - 8) = -2(-48) = 96
\]
Answer: \(96\)
---
Expression 5: \(5(y + 3)\)
Substitute \( y = -5 \):
\[
5(-5 + 3) = 5(-2) = -10
\]
Answer: \(-10\)
---
Expression 6: \(-6(-2 - 2c)\)
Substitute \( c = 8 \):
\[
-6(-2 - 2(8)) = -6(-2 - 16) = -6(-18) = 108
\]
Answer: \(108\)
---
Expression 7: \(2(3t - 5)\)
Substitute \( t = 20 \):
\[
2(3(20) - 5) = 2(60 - 5) = 2(55) = 110
\]
Answer: \(110\)
---
Expression 8: \(-4(a - 4)\)
Substitute \( a = 3 \):
\[
-4(3 - 4) = -4(-1) = 4
\]
Answer: \(4\)
---
Expression 9: \(-3(b - 2)\)
Substitute \( b = 5 \):
\[
-3(5 - 2) = -3(3) = -9
\]
Answer: \(-9\)
---
Expression 10: \(3(-1 - 4n)\)
Substitute \( n = 14 \):
\[
3(-1 - 4(14)) = 3(-1 - 56) = 3(-57) = -171
\]
Answer: \(-171\)
---
Expression 11: \(-3(9u + 5)\)
Substitute \( u = 25 \):
\[
-3(9(25) + 5) = -3(225 + 5) = -3(230) = -690
\]
Answer: \(-690\)
---
Expression 12: \(9(z + 4)\)
Substitute \( z = 0.5 \):
\[
9(0.5 + 4) = 9(4.5) = 40.5
\]
Answer: \(40.5\)
---
Expression 13: \(3(-5 - 2t)\)
Substitute \( t = 20 \):
\[
3(-5 - 2(20)) = 3(-5 - 40) = 3(-45) = -135
\]
Answer: \(-135\)
---
Expression 14: \(-3(3 + 6x)\)
Substitute \( x = -2 \):
\[
-3(3 + 6(-2)) = -3(3 - 12) = -3(-9) = 27
\]
Answer: \(27\)
---
Expression 15: \((-8 + u)6\)
Substitute \( u = 25 \):
\[
(-8 + 25)6 = (17)6 = 102
\]
Answer: \(102\)
---
Expression 16: \(-(5 - 2c)\)
Substitute \( c = 8 \):
\[
-(5 - 2(8)) = -(5 - 16) = -(-11) = 11
\]
Answer: \(11\)
---
Expression 17: \((-z + 4)2\)
Substitute \( z = 0.5 \):
\[
(-0.5 + 4)2 = (3.5)2 = 7
\]
Answer: \(7\)
---
Expression 18: \(2(3 + 4y)\)
Substitute \( y = -5 \):
\[
2(3 + 4(-5)) = 2(3 - 20) = 2(-17) = -34
\]
Answer: \(-34\)
---
Expression 19: \(2(4 + 3y)\)
Substitute \( y = -5 \):
\[
2(4 + 3(-5)) = 2(4 - 15) = 2(-11) = -22
\]
Answer: \(-22\)
---
Expression 20: \(5(2x + 0)\)
Substitute \( x = -2 \):
\[
5(2(-2) + 0) = 5(-4) = -20
\]
Answer: \(-20\)
---
Expression 21: \(5(-2t - 6)\)
Substitute \( t = 20 \):
\[
5(-2(20) - 6) = 5(-40 - 6) = 5(-46) = -230
\]
Answer: \(-230\)
---
Final Answers:
\[
\boxed{
\begin{array}{ccc}
-42 & -93 & -128 \\
96 & -10 & 108 \\
110 & 4 & -9 \\
-171 & -690 & 40.5 \\
-135 & 27 & 102 \\
11 & 7 & -34 \\
-22 & -20 & -230 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of evaluating expressions worksheet 6th grade.