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Stells [14]
3 years ago
13

How many solutions are there to this equation 3(x-4)+5-x=2x-7

Mathematics
1 answer:
Svetlanka [38]3 years ago
8 0
3x-12+5-x=2x-7
2x-7 =2x-7

Means there are infinite solutions.
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3 years ago
Solve the inequality both algebraically and graphically. Draw a number line graph of the solution and give interval notation.
Lemur [1.5K]
Finding the solution algebraically

To answer this inequality, we can follow the next steps:

1. Multiply by 7 both sides of the inequality:

7\cdot\frac{(x-7)}{2}

2. Multiply by 2 both sides of the inequality:

7\cdot2\cdot^{\cdot}\frac{(x-7)}{2}

3. Apply the distributive property at the left side of the inequality:

7\cdot x-7\cdot7

4. Add 49 to both sides of the inequality:

7x-49+49

5. Finally, divide both sides of the inequality by 7:

\frac{7x}{7}

We can graph this inequality in the number line as follows:

Notice the parenthesis indicating that the solution is the number below 131/7 (but not equal to 131/7). <em>In interval notation the solution is</em>:

(-\infty,\frac{131}{7})(-\infty,18\frac{5}{7})

Or, approximately:

(-\infty,18.7142857143)

The number 131/7 in decimal is equivalent to 18.7142857143, so the graph of the solution is given by graph A (we can see that there are seven divisions between 18 and 19; since we have that the shaded division is in the 5th division, then, we have 5/7 = 0.714285714286, that is, the decimal part of the above number).

We can express the number 131/7 as a mixed number as follows:

\frac{131}{7}=\frac{126}{7}+\frac{5}{7}=18+\frac{5}{7}=18\frac{5}{7}

Again, <em>notice also the symbol for the left part of the interval notation is a parenthesis since the interval is open at the point 131/7 = 18 + 5/7</em>.

Finding the solution graphically

To find the solution graphically, we can represent the inequality as two lines as follows:

y=\frac{x-7}{2},y=\frac{41}{7}

Then, if we graph the first line, we can find the x- and the y-intercepts to find two points to graph the line. We have that the x- and the y-intercepts are:

The x-intercept is (that is, when y = 0):

0=\frac{x-7}{2}\Rightarrow x-7=0\Rightarrow x=7

Then, the x-intercept is (7, 0), and the y-intercept (the point on the graph when x = 0) is:

y=\frac{x-7}{2}\Rightarrow y=\frac{0-7}{2}\Rightarrow y=-\frac{7}{2}

Then, the y-intercept is (0, -7/2).

The other line is given by:

y=\frac{41}{7}=\frac{35}{7}+\frac{6}{7}=5\frac{6}{7}

With this information, we can graph both lines:

And we can see that the point where the two lines coincide is:

(\frac{131}{7},\frac{41}{7})

Then, <em>the values for x of the line (x-7)/2 [that is, the values of y = (x-7)/2] that are less than y = 41/7, represented as</em>:

\frac{(x-7)}{2}

Are those values of x less than 131/7, or the solution is also (we express the solution as a fraction or a mixed number as follows) (the same solution):

(-\infty,\frac{131}{7})or(-\infty,18\frac{5}{7})

In summary, we have that the solution to the inequality is:

As an inequality:

x

In interval notation:

(-\infty,18\frac{5}{7})or(-\infty,\frac{131}{7})

And the representation of the solution on the number line is (option A):

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Answer:

what equation.?

Step-by-step explanation:

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Tim wants to boil rice on the stove. He needs to use exactly three gallons of water in a pot to boil the rice. Which method shou
MatroZZZ [7]

A. is obviously the most easiest one, as you just have to fill it up 3 times to get 3 gallons.

The next one to measure exactly 3 gallons of water is B), because:

1) the 100-gallon barrel is more than 1 gallon, and is much more harder than 3 gallons.

2) Each person's 'palm' can hold different amounts of water, and so it can vary by the size of the palm.

So IF it cannot be (A), then your next choice is (B), as you only need 768 teaspoons for each gallon.

But, you should report this problem to the teacher, since A is obviously the best choice

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Answer:

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Step-by-step explanation:

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