Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{-7}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7-x } & = & -3 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -3 \color{blue}{+7} \\\Leftrightarrow &-3x & = &4\\\Leftrightarrow & \color{red}{-3}x & = &4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{+4}& = & -13 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4+10x } & = & -13 \color{red}{ -10x }\color{blue}{-4+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & -13 \color{blue}{-4} \\\Leftrightarrow &17x & = &-17\\\Leftrightarrow & \color{red}{17}x & = &-17\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-17}{17} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-2}& = & -4 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2+13x } & = & -4 \color{red}{ -13x }\color{blue}{+2+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -4 \color{blue}{+2} \\\Leftrightarrow &20x & = &-2\\\Leftrightarrow & \color{red}{20}x & = &-2\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-2}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-3}& = & 12 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3-14x } & = & 12 \color{red}{ +14x }\color{blue}{+3-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 12 \color{blue}{+3} \\\Leftrightarrow &-25x & = &15\\\Leftrightarrow & \color{red}{-25}x & = &15\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{15}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{-11}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11-13x } & = & 11 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 11 \color{blue}{+11} \\\Leftrightarrow &-19x & = &22\\\Leftrightarrow & \color{red}{-19}x & = &22\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{22}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{19} } & & \\ & V = \left\{ \frac{-22}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{-3}& = & -15 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3+12x } & = & -15 \color{red}{ -12x }\color{blue}{+3+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -15 \color{blue}{+3} \\\Leftrightarrow &25x & = &-12\\\Leftrightarrow & \color{red}{25}x & = &-12\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-12}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{25} } & & \\ & V = \left\{ \frac{-12}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{-8}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8-7x } & = & -13 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &-3x & = &-5\\\Leftrightarrow & \color{red}{-3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{-12}& = & 9 \color{red}{ -5x } \\\Leftrightarrow & 13x \color{red}{-12}\color{blue}{+12+5x } & = & 9 \color{red}{ -5x }\color{blue}{+12+5x } \\\Leftrightarrow & 13x \color{blue}{+5x } & = & 9 \color{blue}{+12} \\\Leftrightarrow &18x & = &21\\\Leftrightarrow & \color{red}{18}x & = &21\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{21}{18} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-8}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-9x } & = & -14 \color{red}{ +9x }\color{blue}{+8-9x } \\\Leftrightarrow & -13x \color{blue}{-9x } & = & -14 \color{blue}{+8} \\\Leftrightarrow &-22x & = &-6\\\Leftrightarrow & \color{red}{-22}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-22}x}{ \color{blue}{ -22}} & = & \frac{-6}{-22} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-2}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2-x } & = & 7 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 7 \color{blue}{+2} \\\Leftrightarrow &-8x & = &9\\\Leftrightarrow & \color{red}{-8}x & = &9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+6}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6-13x } & = & -13 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -13 \color{blue}{-6} \\\Leftrightarrow &-28x & = &-19\\\Leftrightarrow & \color{red}{-28}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-19}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{19}{28} } & & \\ & V = \left\{ \frac{19}{28} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+5}& = & -6 \color{red}{ +5x } \\\Leftrightarrow & 11x \color{red}{+5}\color{blue}{-5-5x } & = & -6 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & 11x \color{blue}{-5x } & = & -6 \color{blue}{-5} \\\Leftrightarrow &6x & = &-11\\\Leftrightarrow & \color{red}{6}x & = &-11\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-11}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)