Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{+11}& = & -15 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11+11x } & = & -15 \color{red}{ -11x }\color{blue}{-11+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -15 \color{blue}{-11} \\\Leftrightarrow &15x & = &-26\\\Leftrightarrow & \color{red}{15}x & = &-26\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-26}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{15} } & & \\ & V = \left\{ \frac{-26}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-10}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-10}\color{blue}{+10-x } & = & 3 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 3 \color{blue}{+10} \\\Leftrightarrow &5x & = &13\\\Leftrightarrow & \color{red}{5}x & = &13\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{13}{5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+9}& = & -8 \color{red}{ +8x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9-8x } & = & -8 \color{red}{ +8x }\color{blue}{-9-8x } \\\Leftrightarrow & x \color{blue}{-8x } & = & -8 \color{blue}{-9} \\\Leftrightarrow &-7x & = &-17\\\Leftrightarrow & \color{red}{-7}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{17}{7} } & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+6}& = & 8 \color{red}{ +15x } \\\Leftrightarrow & -x \color{red}{+6}\color{blue}{-6-15x } & = & 8 \color{red}{ +15x }\color{blue}{-6-15x } \\\Leftrightarrow & -x \color{blue}{-15x } & = & 8 \color{blue}{-6} \\\Leftrightarrow &-16x & = &2\\\Leftrightarrow & \color{red}{-16}x & = &2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-3}& = & 1 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3-9x } & = & 1 \color{red}{ +9x }\color{blue}{+3-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & 1 \color{blue}{+3} \\\Leftrightarrow &-7x & = &4\\\Leftrightarrow & \color{red}{-7}x & = &4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{-10}& = & 7 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-10}\color{blue}{+10+6x } & = & 7 \color{red}{ -6x }\color{blue}{+10+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 7 \color{blue}{+10} \\\Leftrightarrow &19x & = &17\\\Leftrightarrow & \color{red}{19}x & = &17\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{17}{19} \\\Leftrightarrow & \color{green}{ x = \frac{17}{19} } & & \\ & V = \left\{ \frac{17}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+13}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & x \color{red}{+13}\color{blue}{-13-7x } & = & -10 \color{red}{ +7x }\color{blue}{-13-7x } \\\Leftrightarrow & x \color{blue}{-7x } & = & -10 \color{blue}{-13} \\\Leftrightarrow &-6x & = &-23\\\Leftrightarrow & \color{red}{-6}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-23}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{23}{6} } & & \\ & V = \left\{ \frac{23}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{+7}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & -x \color{red}{+7}\color{blue}{-7-5x } & = & -11 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & -x \color{blue}{-5x } & = & -11 \color{blue}{-7} \\\Leftrightarrow &-6x & = &-18\\\Leftrightarrow & \color{red}{-6}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-18}{-6} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+12}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+12}\color{blue}{-12-x } & = & -4 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -4 \color{blue}{-12} \\\Leftrightarrow &-7x & = &-16\\\Leftrightarrow & \color{red}{-7}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{16}{7} } & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2-x } & = & 15 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 15 \color{blue}{+2} \\\Leftrightarrow &-7x & = &17\\\Leftrightarrow & \color{red}{-7}x & = &17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{7} } & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-14}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{-14}\color{blue}{+14-9x } & = & -14 \color{red}{ +9x }\color{blue}{+14-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & -14 \color{blue}{+14} \\\Leftrightarrow &-5x & = &0\\\Leftrightarrow & \color{red}{-5}x & = &0\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{0}{-5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-11}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-11}\color{blue}{+11-x } & = & 14 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 14 \color{blue}{+11} \\\Leftrightarrow &-4x & = &25\\\Leftrightarrow & \color{red}{-4}x & = &25\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{25}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{4} } & & \\ & V = \left\{ \frac{-25}{4} \right\} & \\\end{align}\)