Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{-11}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-x } & = & -7 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -7 \color{blue}{+11} \\\Leftrightarrow &-6x & = &4\\\Leftrightarrow & \color{red}{-6}x & = &4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+11}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+11}\color{blue}{-11-x } & = & 8 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 8 \color{blue}{-11} \\\Leftrightarrow &-8x & = &-3\\\Leftrightarrow & \color{red}{-8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{+14}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14-x } & = & -7 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -7 \color{blue}{-14} \\\Leftrightarrow &13x & = &-21\\\Leftrightarrow & \color{red}{13}x & = &-21\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-21}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{13} } & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+1}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-11x } & = & 9 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 9 \color{blue}{-1} \\\Leftrightarrow &-18x & = &8\\\Leftrightarrow & \color{red}{-18}x & = &8\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{8}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-2}& = & 15 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2+7x } & = & 15 \color{red}{ -7x }\color{blue}{+2+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 15 \color{blue}{+2} \\\Leftrightarrow &11x & = &17\\\Leftrightarrow & \color{red}{11}x & = &17\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{17}{11} \\\Leftrightarrow & \color{green}{ x = \frac{17}{11} } & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{+14}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-x } & = & -4 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &-8x & = &-18\\\Leftrightarrow & \color{red}{-8}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-18}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{+4}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4-x } & = & 11 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 11 \color{blue}{-4} \\\Leftrightarrow &-3x & = &7\\\Leftrightarrow & \color{red}{-3}x & = &7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{+14}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-x } & = & 4 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &-13x & = &-10\\\Leftrightarrow & \color{red}{-13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-10}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & 13x \color{red}{-10}\color{blue}{+10-7x } & = & -4 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & 13x \color{blue}{-7x } & = & -4 \color{blue}{+10} \\\Leftrightarrow &6x & = &6\\\Leftrightarrow & \color{red}{6}x & = &6\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{6}{6} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{+11}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-x } & = & 10 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 10 \color{blue}{-11} \\\Leftrightarrow &-9x & = &-1\\\Leftrightarrow & \color{red}{-9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-13}& = & -10 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{-13}\color{blue}{+13-5x } & = & -10 \color{red}{ +5x }\color{blue}{+13-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & -10 \color{blue}{+13} \\\Leftrightarrow &-19x & = &3\\\Leftrightarrow & \color{red}{-19}x & = &3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{19} } & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-2}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-2}\color{blue}{+2-5x } & = & -8 \color{red}{ +5x }\color{blue}{+2-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -8 \color{blue}{+2} \\\Leftrightarrow &7x & = &-6\\\Leftrightarrow & \color{red}{7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)