# Thread: Answer the following exercises (polynomial, degree 1)

1. ## Answer the following exercises (polynomial, degree 1)

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

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

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

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

$\displaystyle 86x-4=-14$

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

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

$\displaystyle 86x=-10$

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

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

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

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

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

Step 2: Combine like terms.

$\displaystyle 3t-21=-3t+21$

Step 3: Add 21 to each side.

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

$\displaystyle 3t=-3t+42$

Step 4: Add 3t to both sides.

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

$\displaystyle 6t=42$

Step 5: Finally, divide both sides by 6.

$\displaystyle \boxed{t=7}$

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

3. Oh thank you mate! I feel really stupid right now considering the gravity of the problem...