Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+8}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+8}\color{blue}{-8-x } & = & 14 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 14 \color{blue}{-8} \\\Leftrightarrow &-8x & = &6\\\Leftrightarrow & \color{red}{-8}x & = &6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-12}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-12}\color{blue}{+12-x } & = & -15 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -15 \color{blue}{+12} \\\Leftrightarrow &13x & = &-3\\\Leftrightarrow & \color{red}{13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-9}& = & 15 \color{red}{ +3x } \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9-3x } & = & 15 \color{red}{ +3x }\color{blue}{+9-3x } \\\Leftrightarrow & -8x \color{blue}{-3x } & = & 15 \color{blue}{+9} \\\Leftrightarrow &-11x & = &24\\\Leftrightarrow & \color{red}{-11}x & = &24\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{24}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{11} } & & \\ & V = \left\{ \frac{-24}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-4}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-4}\color{blue}{+4-13x } & = & 5 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 5 \color{blue}{+4} \\\Leftrightarrow &-19x & = &9\\\Leftrightarrow & \color{red}{-19}x & = &9\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{9}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{19} } & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+5}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-x } & = & 3 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 3 \color{blue}{-5} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{-11}& = & 3 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11+11x } & = & 3 \color{red}{ -11x }\color{blue}{+11+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &26x & = &14\\\Leftrightarrow & \color{red}{26}x & = &14\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{14}{26} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-2}& = & 15 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2+13x } & = & 15 \color{red}{ -13x }\color{blue}{+2+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 15 \color{blue}{+2} \\\Leftrightarrow &22x & = &17\\\Leftrightarrow & \color{red}{22}x & = &17\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{17}{22} \\\Leftrightarrow & \color{green}{ x = \frac{17}{22} } & & \\ & V = \left\{ \frac{17}{22} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+13}& = & -15 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+13}\color{blue}{-13+7x } & = & -15 \color{red}{ -7x }\color{blue}{-13+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -15 \color{blue}{-13} \\\Leftrightarrow &11x & = &-28\\\Leftrightarrow & \color{red}{11}x & = &-28\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-28}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{11} } & & \\ & V = \left\{ \frac{-28}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+15}& = & 7 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+15}\color{blue}{-15-9x } & = & 7 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 7 \color{blue}{-15} \\\Leftrightarrow &5x & = &-8\\\Leftrightarrow & \color{red}{5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+14}& = & -8 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14-14x } & = & -8 \color{red}{ +14x }\color{blue}{-14-14x } \\\Leftrightarrow & 11x \color{blue}{-14x } & = & -8 \color{blue}{-14} \\\Leftrightarrow &-3x & = &-22\\\Leftrightarrow & \color{red}{-3}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-22}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{22}{3} } & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{+11}& = & -15 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11-11x } & = & -15 \color{red}{ +11x }\color{blue}{-11-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & -15 \color{blue}{-11} \\\Leftrightarrow &-7x & = &-26\\\Leftrightarrow & \color{red}{-7}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-26}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{26}{7} } & & \\ & V = \left\{ \frac{26}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{-8}& = & -13 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-8}\color{blue}{+8+5x } & = & -13 \color{red}{ -5x }\color{blue}{+8+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &8x & = &-5\\\Leftrightarrow & \color{red}{8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-5}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)