Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{-8}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8-x } & = & -5 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -5 \color{blue}{+8} \\\Leftrightarrow &-15x & = &3\\\Leftrightarrow & \color{red}{-15}x & = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+15}& = & -11 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15-14x } & = & -11 \color{red}{ +14x }\color{blue}{-15-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & -11 \color{blue}{-15} \\\Leftrightarrow &-25x & = &-26\\\Leftrightarrow & \color{red}{-25}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-26}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{26}{25} } & & \\ & V = \left\{ \frac{26}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{-10}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-10}\color{blue}{+10-x } & = & -13 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -13 \color{blue}{+10} \\\Leftrightarrow &-15x & = &-3\\\Leftrightarrow & \color{red}{-15}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-9}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-9}\color{blue}{+9-x } & = & -13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -13 \color{blue}{+9} \\\Leftrightarrow &-11x & = &-4\\\Leftrightarrow & \color{red}{-11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{-14}& = & -13 \color{red}{ +2x } \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14-2x } & = & -13 \color{red}{ +2x }\color{blue}{+14-2x } \\\Leftrightarrow & 15x \color{blue}{-2x } & = & -13 \color{blue}{+14} \\\Leftrightarrow &13x & = &1\\\Leftrightarrow & \color{red}{13}x & = &1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+14}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14-x } & = & -15 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -15 \color{blue}{-14} \\\Leftrightarrow &-11x & = &-29\\\Leftrightarrow & \color{red}{-11}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-29}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{29}{11} } & & \\ & V = \left\{ \frac{29}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-13}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13-x } & = & -3 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -3 \color{blue}{+13} \\\Leftrightarrow &-12x & = &10\\\Leftrightarrow & \color{red}{-12}x & = &10\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{10}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+9}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{+9}\color{blue}{-9-13x } & = & 15 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & 15 \color{blue}{-9} \\\Leftrightarrow &-10x & = &6\\\Leftrightarrow & \color{red}{-10}x & = &6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-14}& = & 9 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14+7x } & = & 9 \color{red}{ -7x }\color{blue}{+14+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 9 \color{blue}{+14} \\\Leftrightarrow &22x & = &23\\\Leftrightarrow & \color{red}{22}x & = &23\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{23}{22} \\\Leftrightarrow & \color{green}{ x = \frac{23}{22} } & & \\ & V = \left\{ \frac{23}{22} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-12}& = & -3 \color{red}{ +5x } \\\Leftrightarrow & 13x \color{red}{-12}\color{blue}{+12-5x } & = & -3 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & 13x \color{blue}{-5x } & = & -3 \color{blue}{+12} \\\Leftrightarrow &8x & = &9\\\Leftrightarrow & \color{red}{8}x & = &9\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{9}{8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+9}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+9}\color{blue}{-9-11x } & = & -11 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -11 \color{blue}{-9} \\\Leftrightarrow &-16x & = &-20\\\Leftrightarrow & \color{red}{-16}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-20}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-2}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-2}\color{blue}{+2-x } & = & -12 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -12 \color{blue}{+2} \\\Leftrightarrow &-5x & = &-10\\\Leftrightarrow & \color{red}{-5}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-10}{-5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)