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Tugas Matematika.pptx
Tugas Matematika
Tentukan Himpunan Penyelesaian dari persamaan berikut:

2X-1=X+4
b.
-3x+4=-x+5
c.
X-4=2X-6
2. Tentukan Himpunan Penyelesaian dari pertidaksamaan berikut:
a.
4X+2 > X-5
b.
-3x+4 < 2x-6
c.
2X-2 > -3X+3
3. Tentukan Himpunan Penyelesaian dari harga mutlak berikut:
a.
|2X-2|=|3X+4|

Tugas Matematika.pptx $\newline$ Tugas Matematika $\newline$ Tentukan Himpunan Penyelesaian dari persamaan berikut: $\newline$ $2 \mathrm{X}-1=\mathrm{X}+4$ $\newline$ b. $-3 x+4=-x+5$ $\newline$ c. $X-4=2 X-6$ $\newline$ $2$ . Tentukan Himpunan Penyelesaian dari pertidaksamaan berikut: $\newline$ a. $4 X+2>X-5$ $\newline$ b. $-3 x+4<2 x-6$ $\newline$ c. $2 X-2>-3 X+3$ $\newline$ $3$ . Tentukan Himpunan Penyelesaian dari harga mutlak berikut: $\newline$ a. $|2 X-2|=|3 X+4|$

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Factor by grouping

Full solution

Q. Tugas Matematika.pptx

\newline

Tugas Matematika

\newline

Tentukan Himpunan Penyelesaian dari persamaan berikut:

\newline

2 \mathrm{X}-1=\mathrm{X}+4

\newline

b.

-3 x+4=-x+5

\newline

c.

X-4=2 X-6

\newline

2

. Tentukan Himpunan Penyelesaian dari pertidaksamaan berikut:

\newline

a.

4 X+2>X-5

\newline

b.

-3 x+4<2 x-6

\newline

c.

2 X-2>-3 X+3

\newline

3

. Tentukan Himpunan Penyelesaian dari harga mutlak berikut:

\newline

a.

|2 X-2|=|3 X+4|

Solve Equation: Solve $2X - 1 = X + 4$ .
Subtract $X$ from both sides: $2X - X - 1 = X - X + 4$ .
Simplify: $X - 1 = 4$ .
Add $1$ to both sides: $X = 4 + 1$ .
Calculate: $X = 5$ .
Solve Inequality: Solve $-3X + 4 = -X + 5$ . Add $3X$ to both sides: $-3X + 3X + 4 = -X + 3X + 5$ . Simplify: $4 = 2X + 5$ . Subtract $5$ from both sides: $4 - 5 = 2X$ . Calculate: $-1 = 2X$ . Divide by $2$ : $X = -\frac{1}{2}$ .
Solve Equation: Solve $X - 4 = 2X - 6$ . $\newline$ Subtract $X$ from both sides: $X - X - 4 = 2X - X - 6$ . $\newline$ Simplify: $-4 = X - 6$ . $\newline$ Add $6$ to both sides: $-4 + 6 = X$ . $\newline$ Calculate: $X = 2$ .
Solve Inequality: Solve $4X + 2 > X - 5$ . $\newline$ Subtract $X$ from both sides: $4X - X + 2 > X - X - 5$ . $\newline$ Simplify: $3X + 2 > -5$ . $\newline$ Subtract $2$ from both sides: $3X > -5 - 2$ . $\newline$ Calculate: $3X > -7$ . $\newline$ Divide by $3$ : $X > -\frac{7}{3}$ .
Solve Inequality: Solve $-3X + 4 < 2X - 6$ . Add $3X$ to both sides: $-3X + 3X + 4 < 2X + 3X - 6$ . Simplify: $4 < 5X - 6$ . Add $6$ to both sides: $4 + 6 < 5X$ . Calculate: $10 < 5X$ . Divide by $5$ : $X > 2$ .
Solve Inequality: Solve $2X - 2 > -3X + 3$ . Add $3X$ to both sides: $2X + 3X - 2 > -3X + 3X + 3$ . Simplify: $5X - 2 > 3$ . Add $2$ to both sides: $5X > 3 + 2$ . Calculate: $5X > 5$ . Divide by $5$ : $X > 1$ .
Solve Absolute Value Equation: Solve $|2X - 2| = |3X + 4|$ . $\newline$ Consider two cases, $2X - 2 = 3X + 4$ and $2X - 2 = -(3X + 4)$ . $\newline$ First case: $2X - 2 = 3X + 4$ . $\newline$ Subtract $2X$ from both sides: $-2 = X + 4$ . $\newline$ Subtract $4$ from both sides: $-6 = X$ .
Solve Absolute Value Equation: Solve $|2X - 2| = |3X + 4|$ . $\newline$ Consider two cases, $2X - 2 = 3X + 4$ and $2X - 2 = -(3X + 4)$ . $\newline$ First case: $2X - 2 = 3X + 4$ . $\newline$ Subtract $2X$ from both sides: $-2 = X + 4$ . $\newline$ Subtract $4$ from both sides: $-6 = X$ .Second case: $2X - 2 = -(3X + 4)$ . $\newline$ Expand the right side: $2X - 2 = -3X - 4$ . $\newline$ Add $2X - 2 = 3X + 4$ $0$ to both sides: $2X - 2 = 3X + 4$ $1$ . $\newline$ Simplify: $2X - 2 = 3X + 4$ $2$ . $\newline$ Add $2X - 2 = 3X + 4$ $3$ to both sides: $2X - 2 = 3X + 4$ $4$ . $\newline$ Divide by $2X - 2 = 3X + 4$ $5$ : $2X - 2 = 3X + 4$ $6$ .

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