Question

1)9x - 7 > x2)- 7x - 10 > - 3x​

Answer 1

Ответ:

$1)x > \frac{7}{8} \\ 2)x > - 2.5$

Объяснение:

$1) 9x - 7 > x \\ 9x - x > 7 \\ 8x > 7 \\ x > \frac{7}{8}$$2) - 7x - 10 > - 3x \\ - 7x + 3x > 10 \\ - 4x > 10 \\ x > - \frac{10}{4} \\ x > - 2.5$

Answer 2

To solve the inequalities:

1. $9x - 7 > x^2$
2. $7x - 10 > -3x$

You can work with each inequality separately:

1. $9x - 7 > x^2$

First, move all terms to one side to set it to zero:

$x^2 - 9x + 7 < 0$

Now, you can factor this quadratic equation:

$(x - 7)(x - 1) < 0$

To find the values of $x$ that satisfy this inequality, you can use a sign chart. Find the critical points where the expression equals zero:

$x - 7 = 0$ -> $x = 7$ $x - 1 = 0$ -> $x = 1$

Now, choose test points in the intervals created by these critical points (i.e., $x < 1$, $1 < x < 7$, and $x > 7$) and determine the sign of the expression in each interval:

• For $x < 1$, pick $x = 0$: $(0 - 7)(0 - 1) < 0$ -> $(-7)(-1) < 0$ -> $7 < 0$ (False)

• For $1 < x < 7$, pick $x = 3$: $(3 - 7)(3 - 1) < 0$ -> $(-4)(2) < 0$ -> $-8 < 0$ (True)

• For $x > 7$, pick $x = 8$: $(8 - 7)(8 - 1) < 0$ -> $(1)(7) < 0$ -> $7 < 0$ (False)

So, the solution to $9x - 7 > x^2$ is $1 < x < 7$.

2. $7x - 10 > -3x$

First, add $3x$ to both sides:

$7x + 3x - 10 > 0$

Simplify the left side:

$10x - 10 > 0$

Now, add 10 to both sides:

$10x > 10$

Finally, divide both sides by 10:

$x > 1$

So, the solution to $7x - 10 > -3x$ is $x > 1$.

In summary:

1. $9x - 7 > x^2$ has the solution $1 < x < 7$.
2. $7x - 10 > -3x$ has the solution $x > 1$.