Answer the following exercises (polynomial, degree 1)

Quote:

Originally Posted by Julian.Ignacio

1) 92x-4=6x-14
2) 3*(t-7)=5*(3-t)+2t+6
3) 0.25R+2=0.75R+5
4) 4+x/4-(x-4)=x-3/2-5x+1/6

Hi Julian.Ignacio,

Let me get you started with the first two, and then you show us how you might start the other two.

1. ${\color{blue}92x-4=6x-14}$

Step 1: Subtract 6x from both sides of the equation to get the variable to one side of the equation.

$92x{\color{red}-6x}-4=6x{\color{red}-6x}-14$

$86x-4=-14$

Step 2: Add 4 to both sides to isolate the variable (get it to one side by itself).

$86x-4{\color{red}+4}=-14{\color{red}+4}$

$86x=-10$

Step 3: Finally, divide both sides by 86 and simplify.

$x=-\frac{10}{86}=\boxed{-\frac{5}{43}}$

2. ${\color{blue}3(t-7)=5(3-t)+2t+6}$

Step 1: Use the distributive property to simplify the equation.

$3t-21=15-5t+2t+6$

Step 2: Combine like terms.

$3t-21=-3t+21$

Step 3: Add 21 to each side.

$3t-21{\color{red}+21}=-3t+21{\color{red}+21}$

$3t=-3t+42$

Step 4: Add 3t to both sides.

$3t{\color{red}+3t}=-3t{\color{red}+3t}+42$

$6t=42$

Step 5: Finally, divide both sides by 6.

$\boxed{t=7}$

Good luck with the other two. Let us know if you have problems. Show us some of your work.