Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+15}& = & 14 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+15}\color{blue}{-15-9x } & = & 14 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 14 \color{blue}{-15} \\\Leftrightarrow &-17x & = &-1\\\Leftrightarrow & \color{red}{-17}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-1}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{1}{17} } & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+9}& = & -6 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+9}\color{blue}{-9+15x } & = & -6 \color{red}{ -15x }\color{blue}{-9+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -6 \color{blue}{-9} \\\Leftrightarrow &19x & = &-15\\\Leftrightarrow & \color{red}{19}x & = &-15\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-15}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{19} } & & \\ & V = \left\{ \frac{-15}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{+1}& = & 8 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+1}\color{blue}{-1-7x } & = & 8 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & 8 \color{blue}{-1} \\\Leftrightarrow &-5x & = &7\\\Leftrightarrow & \color{red}{-5}x & = &7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-4}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-x } & = & 14 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 14 \color{blue}{+4} \\\Leftrightarrow &-11x & = &18\\\Leftrightarrow & \color{red}{-11}x & = &18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{+6}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+6}\color{blue}{-6-x } & = & -3 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -3 \color{blue}{-6} \\\Leftrightarrow &-7x & = &-9\\\Leftrightarrow & \color{red}{-7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-11}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-11}\color{blue}{+11-7x } & = & -13 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & -13 \color{blue}{+11} \\\Leftrightarrow &-10x & = &-2\\\Leftrightarrow & \color{red}{-10}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-14}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{-14}\color{blue}{+14-11x } & = & -5 \color{red}{ +11x }\color{blue}{+14-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -5 \color{blue}{+14} \\\Leftrightarrow &-9x & = &9\\\Leftrightarrow & \color{red}{-9}x & = &9\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{9}{-9} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+5}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-x } & = & 6 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 6 \color{blue}{-5} \\\Leftrightarrow &-15x & = &1\\\Leftrightarrow & \color{red}{-15}x & = &1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+9}& = & -15 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{+9}\color{blue}{-9-9x } & = & -15 \color{red}{ +9x }\color{blue}{-9-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & -15 \color{blue}{-9} \\\Leftrightarrow &x & = &-24\\\Leftrightarrow & \color{red}{}x & = &-24\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -24 \\\Leftrightarrow & \color{green}{ x = -24 } & & \\ & V = \left\{ -24 \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-10}& = & 4 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{-10}\color{blue}{+10-6x } & = & 4 \color{red}{ +6x }\color{blue}{+10-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 4 \color{blue}{+10} \\\Leftrightarrow &-17x & = &14\\\Leftrightarrow & \color{red}{-17}x & = &14\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{14}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{17} } & & \\ & V = \left\{ \frac{-14}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-7}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7-13x } & = & -14 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & -14 \color{blue}{+7} \\\Leftrightarrow &-3x & = &-7\\\Leftrightarrow & \color{red}{-3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{-14}& = & -4 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14+5x } & = & -4 \color{red}{ -5x }\color{blue}{+14+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -4 \color{blue}{+14} \\\Leftrightarrow &8x & = &10\\\Leftrightarrow & \color{red}{8}x & = &10\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{10}{8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)