Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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