Question

1. solve the following equations:

a) ( 6w = 32 )
b) ( 5y = 35 )
c) ( -2x = 18 )
d) ( \frac{k}{4} = 3 )
b) ( \frac{n}{2} = 8 )
c) ( \frac{r}{-5} = -2 )
(and other equations with handwritten solutions around, like ( h + 1 = 7 ), ( p + 5 = 6 ), ( r - 9 = 2 ), ( t - 3 = 5 ), ( x + 8 = 12 ), ( m + 7 = 10 ) etc. with some handwritten answers)

Explanation:

Let's solve each equation one by one:

Part 2: Solve the following equations

a) \( 6w = 32 \)

Step 1: Isolate \( w \)

Divide both sides by 6: \( w=\frac{32}{6}=\frac{16}{3}\approx5.33 \)

b) \( 5y = 35 \)

Step 1: Isolate \( y \)

Divide both sides by 5: \( y = \frac{35}{5}=7 \)

c) \( -2x = 18 \)

Step 1: Isolate \( x \)

Divide both sides by -2: \( x=\frac{18}{-2}=-9 \)

d) \( \frac{k}{4}=3 \)

Step 1: Isolate \( k \)

Multiply both sides by 4: \( k = 3\times4 = 12 \)

e) \( \frac{n}{2}=8 \)

Step 1: Isolate \( n \)

Multiply both sides by 2: \( n=8\times2 = 16 \)

f) \( \frac{r}{-5}=-2 \)

Step 1: Isolate \( r \)

Multiply both sides by -5: \( r=-2\times(-5)=10 \)

Other equations (from the left side, maybe part 1? Let's solve them too)

g) \( h + 1=7 \)

Step 1: Isolate \( h \)

Subtract 1 from both sides: \( h=7 - 1=6 \)

h) \( x + 8=12 \)

Step 1: Isolate \( x \)

Subtract 8 from both sides: \( x=12 - 8 = 4 \)

i) \( p + 5=6 \)

Step 1: Isolate \( p \)

Subtract 5 from both sides: \( p=6 - 5=1 \)

j) \( r-9 = 2 \)

Step 1: Isolate \( r \)

Add 9 to both sides: \( r=2 + 9=11 \)

k) \( t-3 = 5 \)

Step 1: Isolate \( t \)

Add 3 to both sides: \( t=5 + 3=8 \)

l) \( m + 7=10 \)

Step 1: Isolate \( m \)

Subtract 7 from both sides: \( m=10 - 7=3 \)

m) \( p-4 = 2 \)

Step 1: Isolate \( p \)

Add 4 to both sides: \( p=2 + 4=6 \)

n) \( h + 1=7 \) (already solved as \( h = 6 \))

Final Answers:

• \( 6w = 32 \): \( \boldsymbol{w=\frac{16}{3}} \)
• \( 5y = 35 \): \( \boldsymbol{y = 7} \)
• \( -2x = 18 \): \( \boldsymbol{x=-9} \)
• \( \frac{k}{4}=3 \): \( \boldsymbol{k = 12} \)
• \( \frac{n}{2}=8 \): \( \boldsymbol{n = 16} \)
• \( \frac{r}{-5}=-2 \): \( \boldsymbol{r = 10} \)
• \( h + 1=7 \): \( \boldsymbol{h = 6} \)
• \( x + 8=12 \): \( \boldsymbol{x = 4} \)
• \( p + 5=6 \): \( \boldsymbol{p = 1} \)
• \( r-9 = 2 \): \( \boldsymbol{r = 11} \)
• \( t-3 = 5 \): \( \boldsymbol{t = 8} \)
• \( m + 7=10 \): \( \boldsymbol{m = 3} \)
• \( p-4 = 2 \): \( \boldsymbol{p = 6} \)

Answer:

Let's solve each equation one by one:

Part 2: Solve the following equations

a) \( 6w = 32 \)

Step 1: Isolate \( w \)

Divide both sides by 6: \( w=\frac{32}{6}=\frac{16}{3}\approx5.33 \)

b) \( 5y = 35 \)

Step 1: Isolate \( y \)

Divide both sides by 5: \( y = \frac{35}{5}=7 \)

c) \( -2x = 18 \)

Step 1: Isolate \( x \)

Divide both sides by -2: \( x=\frac{18}{-2}=-9 \)

d) \( \frac{k}{4}=3 \)

Step 1: Isolate \( k \)

Multiply both sides by 4: \( k = 3\times4 = 12 \)

e) \( \frac{n}{2}=8 \)

Step 1: Isolate \( n \)

Multiply both sides by 2: \( n=8\times2 = 16 \)

f) \( \frac{r}{-5}=-2 \)

Step 1: Isolate \( r \)

Multiply both sides by -5: \( r=-2\times(-5)=10 \)

Other equations (from the left side, maybe part 1? Let's solve them too)

g) \( h + 1=7 \)

Step 1: Isolate \( h \)

Subtract 1 from both sides: \( h=7 - 1=6 \)

h) \( x + 8=12 \)

Step 1: Isolate \( x \)

Subtract 8 from both sides: \( x=12 - 8 = 4 \)

i) \( p + 5=6 \)

Step 1: Isolate \( p \)

Subtract 5 from both sides: \( p=6 - 5=1 \)

j) \( r-9 = 2 \)

Step 1: Isolate \( r \)

Add 9 to both sides: \( r=2 + 9=11 \)

k) \( t-3 = 5 \)

Step 1: Isolate \( t \)

Add 3 to both sides: \( t=5 + 3=8 \)

l) \( m + 7=10 \)

Step 1: Isolate \( m \)

Subtract 7 from both sides: \( m=10 - 7=3 \)

m) \( p-4 = 2 \)

Step 1: Isolate \( p \)

Add 4 to both sides: \( p=2 + 4=6 \)

n) \( h + 1=7 \) (already solved as \( h = 6 \))

Final Answers:

• \( 6w = 32 \): \( \boldsymbol{w=\frac{16}{3}} \)
• \( 5y = 35 \): \( \boldsymbol{y = 7} \)
• \( -2x = 18 \): \( \boldsymbol{x=-9} \)
• \( \frac{k}{4}=3 \): \( \boldsymbol{k = 12} \)
• \( \frac{n}{2}=8 \): \( \boldsymbol{n = 16} \)
• \( \frac{r}{-5}=-2 \): \( \boldsymbol{r = 10} \)
• \( h + 1=7 \): \( \boldsymbol{h = 6} \)
• \( x + 8=12 \): \( \boldsymbol{x = 4} \)
• \( p + 5=6 \): \( \boldsymbol{p = 1} \)
• \( r-9 = 2 \): \( \boldsymbol{r = 11} \)
• \( t-3 = 5 \): \( \boldsymbol{t = 8} \)
• \( m + 7=10 \): \( \boldsymbol{m = 3} \)
• \( p-4 = 2 \): \( \boldsymbol{p = 6} \)