Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-13}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & -x \color{red}{-13}\color{blue}{+13-11x } & = & -2 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & -x \color{blue}{-11x } & = & -2 \color{blue}{+13} \\\Leftrightarrow &-12x & = &11\\\Leftrightarrow & \color{red}{-12}x & = &11\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{11}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{12} } & & \\ & V = \left\{ \frac{-11}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-6}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{-6}\color{blue}{+6-7x } & = & -12 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & -12 \color{blue}{+6} \\\Leftrightarrow &-4x & = &-6\\\Leftrightarrow & \color{red}{-4}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-6}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{-4}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4-11x } & = & -3 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & -3 \color{blue}{+4} \\\Leftrightarrow &-7x & = &1\\\Leftrightarrow & \color{red}{-7}x & = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-13}& = & -11 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-13}\color{blue}{+13-8x } & = & -11 \color{red}{ +8x }\color{blue}{+13-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -11 \color{blue}{+13} \\\Leftrightarrow &-23x & = &2\\\Leftrightarrow & \color{red}{-23}x & = &2\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{2}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{23} } & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-6}& = & -15 \color{red}{ -15x } \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6+15x } & = & -15 \color{red}{ -15x }\color{blue}{+6+15x } \\\Leftrightarrow & 13x \color{blue}{+15x } & = & -15 \color{blue}{+6} \\\Leftrightarrow &28x & = &-9\\\Leftrightarrow & \color{red}{28}x & = &-9\\\Leftrightarrow & \frac{\color{red}{28}x}{ \color{blue}{ 28}} & = & \frac{-9}{28} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{28} } & & \\ & V = \left\{ \frac{-9}{28} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-1}& = & -8 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{-1}\color{blue}{+1+11x } & = & -8 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & -8 \color{blue}{+1} \\\Leftrightarrow &25x & = &-7\\\Leftrightarrow & \color{red}{25}x & = &-7\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-7}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{25} } & & \\ & V = \left\{ \frac{-7}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-1}& = & -2 \color{red}{ -2x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1+2x } & = & -2 \color{red}{ -2x }\color{blue}{+1+2x } \\\Leftrightarrow & -x \color{blue}{+2x } & = & -2 \color{blue}{+1} \\\Leftrightarrow &x & = &-1\\\Leftrightarrow & \color{red}{}x & = &-1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -1 \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+2}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+2}\color{blue}{-2-x } & = & 12 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 12 \color{blue}{-2} \\\Leftrightarrow &7x & = &10\\\Leftrightarrow & \color{red}{7}x & = &10\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{10}{7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-10}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-10}\color{blue}{+10-x } & = & -13 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & -13 \color{blue}{+10} \\\Leftrightarrow &6x & = &-3\\\Leftrightarrow & \color{red}{6}x & = &-3\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-3}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{-13}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13-x } & = & 10 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 10 \color{blue}{+13} \\\Leftrightarrow &-4x & = &23\\\Leftrightarrow & \color{red}{-4}x & = &23\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{23}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{4} } & & \\ & V = \left\{ \frac{-23}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-4}& = & -12 \color{red}{ +3x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4-3x } & = & -12 \color{red}{ +3x }\color{blue}{+4-3x } \\\Leftrightarrow & 13x \color{blue}{-3x } & = & -12 \color{blue}{+4} \\\Leftrightarrow &10x & = &-8\\\Leftrightarrow & \color{red}{10}x & = &-8\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-8}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{-2}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-2}\color{blue}{+2+13x } & = & -5 \color{red}{ -13x }\color{blue}{+2+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -5 \color{blue}{+2} \\\Leftrightarrow &23x & = &-3\\\Leftrightarrow & \color{red}{23}x & = &-3\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-3}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{23} } & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)