both lines will intersect at x = 2
Explanation:Given:
-3x + 5 and 1.5x - 4
To get the point of intersection, we can plot the graphs of both expressions or we can equate both equations
Equating both expressions:
-3x + 5 = 1.5x - 4
[tex]\begin{gathered} \text{collect like terms by adding 3x to both sides:} \\ -3x\text{ + 3x + 5 =1.5x +3x - 4} \\ 5\text{ = 4.5x - 4} \\ \\ \text{Add 4 to both sides:} \\ 5\text{ + 4 = 4.5x - 4 + 4} \\ 9\text{ = 4.5x} \end{gathered}[/tex][tex]\begin{gathered} \text{divide both sides by 4.5:} \\ \frac{9}{4.5}\text{ = }\frac{4.5x}{4.5} \\ 2\text{ = x} \end{gathered}[/tex]Point of intersection is when both lines have same value
Hence, both lines will intersect at x = 2
