5|6-5x|=15x-35 2|3x-7|=10x-8 1/4|4x+7|=8x+16 Ok for 5|6-5x|=15x-35 first simplify it by dividing both sides by 5 Then check the intervals where 6-5x>0 then where 6-5x 6/5 the LHS(left hand side) is +. Setting 6-5x=3x-7 means 8x=13 or x=13/8 However, the RHS is positive when X>7/3 so there is no solution when x>6/5 If x 0 means x>7/3 so no solution here either. You could also verify this by graphing too. The LHS and RHS can sometimes be zero at the same time, so check the valuse that make them both 0 too. For this problem the LHS is 0 at 6/5 but the RHS isn't. Conclude no solution for this one.

For the equation 5|6-5x| = 15x-35, we can solve it step-by-step as follows: Step 1: Divide both sides of the equation by 5 to simplify it: |6-5x| = 3x - 7 Step 2: Determine the intervals where the expression inside the absolute values is positive (greater than zero) and negative (less than zero). When 6-5x > 0, we have 6 > 5x, which implies x 6/5. So, we have two intervals: x 6/5. Step 3: Solve the equation separately for each interval. For x 0. But when x = 13/8, 3(13/8) - 7 = 39/8 - 7 = -5/8 which is less than zero. Therefore, there is no solution in this interval. For x > 6/5, we still remove the absolute value signs and get: -(6-5x) = 3x - 7. Solving this equation, we have: 2x = -1, which implies x = -1/2. However, for x > 6/5, we also need to check the condition 3x - 7 > 0. And when x = -1/2, 3(-1/2) - 7 = -3/2 - 7 = -17/2 which is also less than zero. So, there is no solution in this interval as well. Therefore, the answer to the original equation 5|6-5x| = 15x-35 is 'no solution'.

I'm not quite sure about these problems. I know how to do them, but it seems that I get the wrong answer. Maybe I'm supposed to get 'no solution' but I'm not sure. Could someone please help me with them?

5|6-5x|=15x-35
2|3x-7|=10x-8
1/4|4x+7|=8x+16

Ok for
5|6-5x|=15x-35
first simplify it by dividing both sides by 5
Then check the intervals where
6-5x>0 then where 6-5x<0.
In other words, find where the expression in the absolute values is 0 and divide the interval into two parts there. Since the other 2 problems are similar I'll walk through the first one.
You should get
|6-5x|=3x-7 when you divide the 5's out. Then we look where
6-5x=0 which is 6/5
When x>6/5 the LHS(left hand side) is +. Setting
6-5x=3x-7 means 8x=13 or x=13/8
However, the RHS is positive when
X>7/3 so there is no solution when x>6/5
If x<6/5 then |6-5x|=3x-7
-(6-5x)=3x-7 so
-6+5x=3x-7 , 2x=-1 and x=-1/2
Again, 3x-7>0 means x>7/3 so no solution here either.
You could also verify this by graphing too.
The LHS and RHS can sometimes be zero at the same time, so check the valuse that make them both 0 too. For this problem the LHS is 0 at 6/5 but the RHS isn't. Conclude no solution for this one.

3 answers

5x-6+-3x-7

(-16)^-2/3

For the equation 5|6-5x| = 15x-35, we can solve it step-by-step as follows:

Step 1: Divide both sides of the equation by 5 to simplify it:
|6-5x| = 3x - 7

Step 2: Determine the intervals where the expression inside the absolute values is positive (greater than zero) and negative (less than zero).

When 6-5x > 0, we have 6 > 5x, which implies x < 6/5.

When 6-5x < 0, we have 6 < 5x, which implies x > 6/5.

So, we have two intervals: x < 6/5 and x > 6/5.

Step 3: Solve the equation separately for each interval.

For x < 6/5, we can remove the absolute value signs and obtain: 6-5x = 3x - 7.

Solving this equation, we get: 8x = 13, which implies x = 13/8.

However, for x < 6/5, we must also check the condition 3x - 7 > 0.
But when x = 13/8, 3(13/8) - 7 = 39/8 - 7 = -5/8 which is less than zero.

Therefore, there is no solution in this interval.

For x > 6/5, we still remove the absolute value signs and get: -(6-5x) = 3x - 7.

Solving this equation, we have: 2x = -1, which implies x = -1/2.

However, for x > 6/5, we also need to check the condition 3x - 7 > 0.
And when x = -1/2, 3(-1/2) - 7 = -3/2 - 7 = -17/2 which is also less than zero.

So, there is no solution in this interval as well.

Therefore, the answer to the original equation 5|6-5x| = 15x-35 is 'no solution'.