Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{-7}& = & -3 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7+13x } & = & -3 \color{red}{ -13x }\color{blue}{+7+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -3 \color{blue}{+7} \\\Leftrightarrow &24x & = &4\\\Leftrightarrow & \color{red}{24}x & = &4\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{4}{24} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{-2}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-2}\color{blue}{+2-x } & = & -6 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -6 \color{blue}{+2} \\\Leftrightarrow &-6x & = &-4\\\Leftrightarrow & \color{red}{-6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-12}& = & 10 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{-12}\color{blue}{+12+2x } & = & 10 \color{red}{ -2x }\color{blue}{+12+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & 10 \color{blue}{+12} \\\Leftrightarrow &7x & = &22\\\Leftrightarrow & \color{red}{7}x & = &22\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{22}{7} \\\Leftrightarrow & \color{green}{ x = \frac{22}{7} } & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{-11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-11}\color{blue}{+11-x } & = & 13 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 13 \color{blue}{+11} \\\Leftrightarrow &-9x & = &24\\\Leftrightarrow & \color{red}{-9}x & = &24\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{24}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-11}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{-11}\color{blue}{+11-x } & = & 12 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & 12 \color{blue}{+11} \\\Leftrightarrow &10x & = &23\\\Leftrightarrow & \color{red}{10}x & = &23\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{23}{10} \\\Leftrightarrow & \color{green}{ x = \frac{23}{10} } & & \\ & V = \left\{ \frac{23}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{-15}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15-11x } & = & -6 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & -6 \color{blue}{+15} \\\Leftrightarrow &-18x & = &9\\\Leftrightarrow & \color{red}{-18}x & = &9\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{9}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+6}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+6}\color{blue}{-6-x } & = & 1 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 1 \color{blue}{-6} \\\Leftrightarrow &-8x & = &-5\\\Leftrightarrow & \color{red}{-8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-14}& = & 13 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-14}\color{blue}{+14+13x } & = & 13 \color{red}{ -13x }\color{blue}{+14+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 13 \color{blue}{+14} \\\Leftrightarrow &20x & = &27\\\Leftrightarrow & \color{red}{20}x & = &27\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{27}{20} \\\Leftrightarrow & \color{green}{ x = \frac{27}{20} } & & \\ & V = \left\{ \frac{27}{20} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+1}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+1}\color{blue}{-1-x } & = & 5 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 5 \color{blue}{-1} \\\Leftrightarrow &-7x & = &4\\\Leftrightarrow & \color{red}{-7}x & = &4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-15}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-x } & = & -11 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -11 \color{blue}{+15} \\\Leftrightarrow &-7x & = &4\\\Leftrightarrow & \color{red}{-7}x & = &4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+12}& = & 7 \color{red}{ +5x } \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12-5x } & = & 7 \color{red}{ +5x }\color{blue}{-12-5x } \\\Leftrightarrow & 13x \color{blue}{-5x } & = & 7 \color{blue}{-12} \\\Leftrightarrow &8x & = &-5\\\Leftrightarrow & \color{red}{8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-5}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-11}& = & -4 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11-2x } & = & -4 \color{red}{ +2x }\color{blue}{+11-2x } \\\Leftrightarrow & -x \color{blue}{-2x } & = & -4 \color{blue}{+11} \\\Leftrightarrow &-3x & = &7\\\Leftrightarrow & \color{red}{-3}x & = &7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)