Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-4}& = & -15 \color{red}{ +9x } \\\Leftrightarrow & -13x \color{red}{-4}\color{blue}{+4-9x } & = & -15 \color{red}{ +9x }\color{blue}{+4-9x } \\\Leftrightarrow & -13x \color{blue}{-9x } & = & -15 \color{blue}{+4} \\\Leftrightarrow &-22x & = &-11\\\Leftrightarrow & \color{red}{-22}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-22}x}{ \color{blue}{ -22}} & = & \frac{-11}{-22} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{-7}& = & -3 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7+3x } & = & -3 \color{red}{ -3x }\color{blue}{+7+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -3 \color{blue}{+7} \\\Leftrightarrow &13x & = &4\\\Leftrightarrow & \color{red}{13}x & = &4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{-12}& = & -4 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12-9x } & = & -4 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & -4 \color{blue}{+12} \\\Leftrightarrow &-5x & = &8\\\Leftrightarrow & \color{red}{-5}x & = &8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+13}& = & 15 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+13}\color{blue}{-13-11x } & = & 15 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+12}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-x } & = & -12 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -12 \color{blue}{-12} \\\Leftrightarrow &-5x & = &-24\\\Leftrightarrow & \color{red}{-5}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-24}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{24}{5} } & & \\ & V = \left\{ \frac{24}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-9}& = & -13 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9+11x } & = & -13 \color{red}{ -11x }\color{blue}{+9+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & -13 \color{blue}{+9} \\\Leftrightarrow &20x & = &-4\\\Leftrightarrow & \color{red}{20}x & = &-4\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-4}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+1}& = & -4 \color{red}{ -5x } \\\Leftrightarrow & x \color{red}{+1}\color{blue}{-1+5x } & = & -4 \color{red}{ -5x }\color{blue}{-1+5x } \\\Leftrightarrow & x \color{blue}{+5x } & = & -4 \color{blue}{-1} \\\Leftrightarrow &6x & = &-5\\\Leftrightarrow & \color{red}{6}x & = &-5\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-5}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+12}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+12}\color{blue}{-12-x } & = & -2 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -2 \color{blue}{-12} \\\Leftrightarrow &-8x & = &-14\\\Leftrightarrow & \color{red}{-8}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-14}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+15}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15-x } & = & -9 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -9 \color{blue}{-15} \\\Leftrightarrow &-14x & = &-24\\\Leftrightarrow & \color{red}{-14}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-24}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-8}& = & -1 \color{red}{ -15x } \\\Leftrightarrow & -x \color{red}{-8}\color{blue}{+8+15x } & = & -1 \color{red}{ -15x }\color{blue}{+8+15x } \\\Leftrightarrow & -x \color{blue}{+15x } & = & -1 \color{blue}{+8} \\\Leftrightarrow &14x & = &7\\\Leftrightarrow & \color{red}{14}x & = &7\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{7}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{+12}& = & -12 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{+12}\color{blue}{-12-2x } & = & -12 \color{red}{ +2x }\color{blue}{-12-2x } \\\Leftrightarrow & -x \color{blue}{-2x } & = & -12 \color{blue}{-12} \\\Leftrightarrow &-3x & = &-24\\\Leftrightarrow & \color{red}{-3}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-24}{-3} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+9}& = & 5 \color{red}{ -9x } \\\Leftrightarrow & 7x \color{red}{+9}\color{blue}{-9+9x } & = & 5 \color{red}{ -9x }\color{blue}{-9+9x } \\\Leftrightarrow & 7x \color{blue}{+9x } & = & 5 \color{blue}{-9} \\\Leftrightarrow &16x & = &-4\\\Leftrightarrow & \color{red}{16}x & = &-4\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-4}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)