Question

i can solve equations, inequalities, set up equations for word problems, and solve literal equations.

1. ( 4(x - 8) = 4x - 32 ) (handwritten: ( 4x - 32 = 4x - 32 ))
2. ( 7x - 8 > 6x - 11 ) (handwritten: ( 7x - 8 > 6x - 11 ))
3. solve ( x - 2y = 1 ), for ( y )
4. solve ( d + 3n = 1 ), for ( n )
5. the posson’s started with 148 newborn diapers and went through 8 diapers a day. the titzer’s had 100 diapers and went through 4 diapers a day. when will they have the same number of diapers?
6. rectangles the formula ( p = 2ell + 2w ) represents the perimeter of a rectangle. in this formula, ( ell ) is the length of the rectangle and ( w ) is the width.

a. solve the formula for ( ell ).
b. find the length when the width is 4 meters and the perimeter is 36 meters.

Explanation:

Problem 19: \( 4(x - 8)=4x - 32 \)

Step 1: Expand the left - hand side

Using the distributive property \( a(b - c)=ab - ac \), where \( a = 4 \), \( b=x \) and \( c = 8 \), we get \( 4x-32=4x - 32 \)

Step 2: Subtract \( 4x \) from both sides

\( 4x-32-4x=4x - 32-4x \), which simplifies to \( - 32=-32 \)
This is an identity, which means the equation is true for all real values of \( x \).

Step 1: Subtract \( 6x \) from both sides

\( 7x-6x-8>6x - 6x-11 \), which gives \( x - 8>-11 \)

Step 2: Add 8 to both sides

\( x-8 + 8>-11 + 8 \), so \( x>-3 \)

Step 1: Subtract \( x \) from both sides

\( x-x - 2y=1 - x \), which simplifies to \( - 2y=1 - x \)

Step 2: Divide both sides by - 2

\( y=\frac{x - 1}{2}=\frac{1}{2}x-\frac{1}{2} \)

Answer:

All real numbers

Problem 20: \( 7x-8>6x - 11 \)