Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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