Absolutely! Let's go through each of the number sentences step by step.
### 1. [tex]\( a + 5 = 17 \)[/tex]
We'll solve for [tex]\( a \)[/tex]:
[tex]\[ a + 5 = 17 \][/tex]
Subtracting 5 from both sides:
[tex]\[ a = 17 - 5 \][/tex]
[tex]\[ a = 12 \][/tex]
### 1.2 [tex]\( a - 5 = 22 \)[/tex]
We'll solve for [tex]\( a \)[/tex]:
[tex]\[ a - 5 = 22 \][/tex]
Adding 5 to both sides:
[tex]\[ a = 22 + 5 \][/tex]
[tex]\[ a = 27 \][/tex]
### 1.39 [tex]\( 39 \times c + 7 = 52 \)[/tex]
We'll solve for [tex]\( c \)[/tex]:
[tex]\[ 39c + 7 = 52 \][/tex]
Subtracting 7 from both sides:
[tex]\[ 39c = 52 - 7 \][/tex]
[tex]\[ 39c = 45 \][/tex]
Dividing both sides by 39:
[tex]\[ c = \frac{45}{39} \][/tex]
[tex]\[ c \approx 1.1538461538461537 \][/tex]
### 1.48 [tex]\( 48 \times (c - 2) = 32 \)[/tex]
We'll solve for [tex]\( c \)[/tex]:
[tex]\[ 48(c - 2) = 32 \][/tex]
Dividing both sides by 48:
[tex]\[ c - 2 = \frac{32}{48} \][/tex]
[tex]\[ c - 2 = \frac{2}{3} \][/tex]
Adding 2 to both sides:
[tex]\[ c = \frac{2}{3} + 2 \][/tex]
[tex]\[ c \approx 2.6666666666666665 \][/tex]
### 1.5 [tex]\( \frac{3 + b}{2} = 9 \)[/tex]
We'll solve for [tex]\( b \)[/tex]:
[tex]\[ \frac{3 + b}{2} = 9 \][/tex]
Multiplying both sides by 2:
[tex]\[ 3 + b = 18 \][/tex]
Subtracting 3 from both sides:
[tex]\[ b = 18 - 3 \][/tex]
[tex]\[ b = 15 \][/tex]
### 1.6 [tex]\( \frac{c - 5}{3} = 10 \)[/tex]
We'll solve for [tex]\( c \)[/tex]:
[tex]\[ \frac{c - 5}{3} = 10 \][/tex]
Multiplying both sides by 3:
[tex]\[ c - 5 = 30 \][/tex]
Adding 5 to both sides:
[tex]\[ c = 30 + 5 \][/tex]
[tex]\[ c = 35 \][/tex]
### [tex]\( \frac{3x - 2}{4} = 7 \)[/tex]
We'll solve for [tex]\( x \)[/tex]:
[tex]\[ \frac{3x - 2}{4} = 7 \][/tex]
Multiplying both sides by 4:
[tex]\[ 3x - 2 = 28 \][/tex]
Adding 2 to both sides:
[tex]\[ 3x = 30 \][/tex]
Dividing both sides by 3:
[tex]\[ x = \frac{30}{3} \][/tex]
[tex]\[ x = 10 \][/tex]
### 1.8 [tex]\( 0.5 \times d + 1 = 2 \)[/tex]
We'll solve for [tex]\( d \)[/tex]:
[tex]\[ 0.5d + 1 = 2 \][/tex]
Subtracting 1 from both sides:
[tex]\[ 0.5d = 1 \][/tex]
Dividing both sides by 0.5:
[tex]\[ d = \frac{1}{0.5} \][/tex]
[tex]\[ d = 2 \][/tex]
### 1.9 [tex]\( 0.2 \times k + 1 = 3 \)[/tex]
We'll solve for [tex]\( k \)[/tex]:
[tex]\[ 0.2k + 1 = 3 \][/tex]
Subtracting 1 from both sides:
[tex]\[ 0.2k = 2 \][/tex]
Dividing both sides by 0.2:
[tex]\[ k = \frac{2}{0.2} \][/tex]
[tex]\[ k = 10 \][/tex]
Thus, the solutions to the number sentences are:
[tex]\[ a = 12 \][/tex]
[tex]\[ a = 27 \][/tex]
[tex]\[ c \approx 1.1538461538461537 \][/tex]
[tex]\[ c \approx 2.6666666666666665 \][/tex]
[tex]\[ b = 15 \][/tex]
[tex]\[ c = 35 \][/tex]
[tex]\[ x = 10 \][/tex]
[tex]\[ d = 2 \][/tex]
[tex]\[ k = 10 \][/tex]
Therefore, the results you provided are consistent with these calculations.
