Solving inequalities with both multiplication and addition

4(x-3)-2< 3-5(x+7)

Can someone take me through this step by step? I do want to solve it on my own. Thank you

4(x-3)-2< 3-5(x+7)

4x-12-2 < 3-5x-35
4x+5x<-32+12
9x < -20
x < -20/9

Sure! I can guide you through the process step-by-step while allowing you to solve the inequality on your own.

Step 1: Distribute on both sides of the inequality:
4(x-3)-2 < 3-5(x+7)

This becomes:
4x - 12 - 2 < 3 - 5x - 35

Simplifying each side:
4x - 14 < -32 - 5x

Step 2: Combine like terms on each side:
4x - 5x - 14 < -32

Simplifying further:
-x - 14 < -32

Step 3: Add 14 to both sides to isolate the variable:
-x - 14 + 14 < -32 + 14

This simplifies to:
-x < -18

Step 4: Since we have a negative coefficient for x, we need to divide both sides of the inequality by -1. Remember that dividing or multiplying by a negative number flips the inequality sign:
(-x) / -1 > (-18) / -1

This gives us:
x > 18

So, the solution to the inequality is x > 18.

I hope this step-by-step explanation helps you solve the inequality on your own. Let me know if you have any further questions!

Of course! I'll guide you step by step through solving the inequality.

Step 1: Distribute the multiplication on both sides of the equation.
On the left side of the equation, distribute the 4 to both terms inside the parentheses:
4(x-3) - 2 becomes 4x - 12 - 2, which simplifies to 4x - 14.
On the right side of the equation, distribute the -5 to both terms inside the parentheses:
3 - 5(x+7) becomes 3 - 5x - 35, which simplifies to -5x - 32.

After simplifying both sides, the inequality becomes:
4x - 14 < -5x - 32

Step 2: Combine like terms.
In this case, we have x terms on both sides. We want to isolate x on one side of the inequality, so let's add 5x to both sides to get rid of the -5x on the right side:
4x - 14 + 5x < -5x - 32 + 5x

Simplifying, we have:
9x - 14 < -32

Step 3: Isolate the variable x.
Next, let's get rid of the constant term -14 on the left side by adding 14 to both sides:
9x - 14 + 14 < -32 + 14

Simplifying, we have:
9x < -18

Step 4: Solve for x.
Finally, divide both sides of the inequality by 9 to solve for x:
(9x)/9 < (-18)/9

Simplifying, we have:
x < -2

So, the solution to the inequality is x < -2.