Answer:
The solution to the equation is x = 1.4. This means that if we plug the value 1.4 into the equation in place of x, the equation will be satisfied.
Step-by-step explanation:
To solve this equations, we need to first evaluate the absolute value expression on the left-hand side of this questions. The absolute value of a number is a non-negative value of the number, regardless of its sign.
To evaluate the absolute value of an expression, we need to consider two cases: When the expression is positive, and when the expression is negative.
In the first case, where the expression is positive, we can simply evaluate the expression as usual. For example if we want to evaluate the absolute value of 2x + 6, we can simply evaluate the expression 2x + 6 to get the result
In the second case, where the expression is negative, we need to take the opposite of the result we would have gotten if the expression was positive. For example, if we want to evaluate the absolute value of -2x - 6, we would first evaluate the expression -2x - 6 to get a result, and then we would take the opposite of that result to get the absolute value.
With this in mind, let's evaluate the absolute value expressions on the left-hand side of the equation:
|2x + 6| - 3 + |3x - 4| = 9
First, we evaluate the absolute value of 2x + 6. Since this expression is positive, we can simply evaluate it to get:
|2x + 6| - 3 + |3x - 4| = 9
2x + 6 - 3 + |3x - 4| = 9
Next, we evaluate the absolute value of 3x - 4. Since this expression is positive, we can simply evaluate it to get:
2x + 6 - 3 + 3x - 4 = 9
5x + 2 = 9
To solve for x, we can now simply subtract 2 from both sides of the equation, and then divide both sides by 5 to get:
5x + 2 - 2 = 9 - 2
5x = 7
x = 7 / 5 = 1.4
Therefore, the solution to the equation is x = 1.4.