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Solve for \( x \).

[tex]\[ 3x = 6x - 2 \][/tex]


Format the following question or task so that it is easier to read. Fix any grammar or spelling errors. Remove phrases that are not part of the question. Do not remove or change LaTeX formatting. Do not change or remove [tex] [/tex] tags. If the question is nonsense, rewrite it so that it makes sense.

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[tex]\[ 5x + 3y = 10 \][/tex] is a line which meets the \( x \)-axis at a point:

A. \((0,3)\)

B. \((3,0)\)

C. \((2,0)\)

D. [tex]\((0,2)\)[/tex]



Answer :

GinnyAnswer
To determine at which point the line \( 5x + 3y = 10 \) meets the \( x \)-axis, we need to find the \( x \)-intercept of the line.

### Finding the \( x \)-intercept

The \( x \)-intercept is the point where the line crosses the \( x \)-axis. At this point, the \( y \)-coordinate is 0. Let's substitute \( y = 0 \) into the equation of the line and solve for \( x \):

[tex]\[ 5x + 3y = 10 \][/tex]
[tex]\[ 5x + 3(0) = 10 \][/tex]
[tex]\[ 5x = 10 \][/tex]
[tex]\[ x = \frac{10}{5} \][/tex]
[tex]\[ x = 2 \][/tex]

So the \( x \)-intercept of the line \( 5x + 3y = 10 \) is at the point \( (2, 0) \).

### Choosing the correct option

Among the given options:
- (a) \( (0, 3) \)
- (b) \( (3, 0) \)
- (c) \( (2, 0) \)
- (d) \( (0, 2) \)

The correct point where the line meets the \( x \)-axis is \( (2, 0) \).

### Conclusion

Therefore, the correct option is:

(c) [tex]\( (2, 0) \)[/tex]

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