Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+9}& = & 9 \color{red}{ +8x } \\\Leftrightarrow & 9x \color{red}{+9}\color{blue}{-9-8x } & = & 9 \color{red}{ +8x }\color{blue}{-9-8x } \\\Leftrightarrow & 9x \color{blue}{-8x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{-3}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3-13x } & = & 14 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & 14 \color{blue}{+3} \\\Leftrightarrow &-16x & = &17\\\Leftrightarrow & \color{red}{-16}x & = &17\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{17}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{16} } & & \\ & V = \left\{ \frac{-17}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{-11}& = & -10 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11+9x } & = & -10 \color{red}{ -9x }\color{blue}{+11+9x } \\\Leftrightarrow & -x \color{blue}{+9x } & = & -10 \color{blue}{+11} \\\Leftrightarrow &8x & = &1\\\Leftrightarrow & \color{red}{8}x & = &1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-11}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-11}\color{blue}{+11-x } & = & -10 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -10 \color{blue}{+11} \\\Leftrightarrow &-16x & = &1\\\Leftrightarrow & \color{red}{-16}x & = &1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{16} } & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-2}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2-x } & = & 9 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 9 \color{blue}{+2} \\\Leftrightarrow &-8x & = &11\\\Leftrightarrow & \color{red}{-8}x & = &11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-15}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-15}\color{blue}{+15-x } & = & 12 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 12 \color{blue}{+15} \\\Leftrightarrow &-4x & = &27\\\Leftrightarrow & \color{red}{-4}x & = &27\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{27}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{4} } & & \\ & V = \left\{ \frac{-27}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+7}& = & -5 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7+4x } & = & -5 \color{red}{ -4x }\color{blue}{-7+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -5 \color{blue}{-7} \\\Leftrightarrow &13x & = &-12\\\Leftrightarrow & \color{red}{13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{-13}& = & -5 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13-5x } & = & -5 \color{red}{ +5x }\color{blue}{+13-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & -5 \color{blue}{+13} \\\Leftrightarrow &-3x & = &8\\\Leftrightarrow & \color{red}{-3}x & = &8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{-2}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & -x \color{red}{-2}\color{blue}{+2-7x } & = & -4 \color{red}{ +7x }\color{blue}{+2-7x } \\\Leftrightarrow & -x \color{blue}{-7x } & = & -4 \color{blue}{+2} \\\Leftrightarrow &-8x & = &-2\\\Leftrightarrow & \color{red}{-8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-5}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-x } & = & -11 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -11 \color{blue}{+5} \\\Leftrightarrow &-7x & = &-6\\\Leftrightarrow & \color{red}{-7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+7}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+7}\color{blue}{-7-x } & = & 6 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 6 \color{blue}{-7} \\\Leftrightarrow &-10x & = &-1\\\Leftrightarrow & \color{red}{-10}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-6}& = & 15 \color{red}{ +8x } \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6-8x } & = & 15 \color{red}{ +8x }\color{blue}{+6-8x } \\\Leftrightarrow & 13x \color{blue}{-8x } & = & 15 \color{blue}{+6} \\\Leftrightarrow &5x & = &21\\\Leftrightarrow & \color{red}{5}x & = &21\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{21}{5} \\\Leftrightarrow & \color{green}{ x = \frac{21}{5} } & & \\ & V = \left\{ \frac{21}{5} \right\} & \\\end{align}\)