Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(9x-9=3+11x\)
2. \(-x+12=2-8x\)
3. \(13x-9=6+x\)
4. \(-6x+3=3+7x\)
5. \(-2x-13=14+x\)
6. \(5x-11=-14-14x\)
7. \(-7x-7=-2+x\)
8. \(-8x-4=1+9x\)
9. \(-14x+13=7+x\)
10. \(x-15=-1-2x\)
11. \(14x-11=-12+9x\)
12. \(9x+10=-13-2x\)

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{-9}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9-11x } & = & 3 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & 9x \color{blue}{-11x } & = & 3 \color{blue}{+9} \\\Leftrightarrow &-2x & = &12\\\Leftrightarrow & \color{red}{-2}x & = &12\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{12}{-2} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{+12}& = & 2 \color{red}{ -8x } \\\Leftrightarrow & -x \color{red}{+12}\color{blue}{-12+8x } & = & 2 \color{red}{ -8x }\color{blue}{-12+8x } \\\Leftrightarrow & -x \color{blue}{+8x } & = & 2 \color{blue}{-12} \\\Leftrightarrow &7x & = &-10\\\Leftrightarrow & \color{red}{7}x & = &-10\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-10}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{-9}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{-9}\color{blue}{+9-x } & = & 6 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &12x & = &15\\\Leftrightarrow & \color{red}{12}x & = &15\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{15}{12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+3}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3-7x } & = & 3 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 3 \color{blue}{-3} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-13}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-13}\color{blue}{+13-x } & = & 14 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 14 \color{blue}{+13} \\\Leftrightarrow &-3x & = &27\\\Leftrightarrow & \color{red}{-3}x & = &27\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{27}{-3} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-11}& = & -14 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-11}\color{blue}{+11+14x } & = & -14 \color{red}{ -14x }\color{blue}{+11+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -14 \color{blue}{+11} \\\Leftrightarrow &19x & = &-3\\\Leftrightarrow & \color{red}{19}x & = &-3\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-3}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{19} } & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{-7}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-7}\color{blue}{+7-x } & = & -2 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -2 \color{blue}{+7} \\\Leftrightarrow &-8x & = &5\\\Leftrightarrow & \color{red}{-8}x & = &5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-4}& = & 1 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4-9x } & = & 1 \color{red}{ +9x }\color{blue}{+4-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 1 \color{blue}{+4} \\\Leftrightarrow &-17x & = &5\\\Leftrightarrow & \color{red}{-17}x & = &5\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{5}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{17} } & & \\ & V = \left\{ \frac{-5}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{+13}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+13}\color{blue}{-13-x } & = & 7 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 7 \color{blue}{-13} \\\Leftrightarrow &-15x & = &-6\\\Leftrightarrow & \color{red}{-15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{-15}& = & -1 \color{red}{ -2x } \\\Leftrightarrow & x \color{red}{-15}\color{blue}{+15+2x } & = & -1 \color{red}{ -2x }\color{blue}{+15+2x } \\\Leftrightarrow & x \color{blue}{+2x } & = & -1 \color{blue}{+15} \\\Leftrightarrow &3x & = &14\\\Leftrightarrow & \color{red}{3}x & = &14\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{14}{3} \\\Leftrightarrow & \color{green}{ x = \frac{14}{3} } & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-11}& = & -12 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-11}\color{blue}{+11-9x } & = & -12 \color{red}{ +9x }\color{blue}{+11-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -12 \color{blue}{+11} \\\Leftrightarrow &5x & = &-1\\\Leftrightarrow & \color{red}{5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+10}& = & -13 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{+10}\color{blue}{-10+2x } & = & -13 \color{red}{ -2x }\color{blue}{-10+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & -13 \color{blue}{-10} \\\Leftrightarrow &11x & = &-23\\\Leftrightarrow & \color{red}{11}x & = &-23\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-23}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{11} } & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)