Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+13}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13-x } & = & 4 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 4 \color{blue}{-13} \\\Leftrightarrow &-11x & = &-9\\\Leftrightarrow & \color{red}{-11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+4}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-7x } & = & 6 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 6 \color{blue}{-4} \\\Leftrightarrow &-20x & = &2\\\Leftrightarrow & \color{red}{-20}x & = &2\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{2}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{-9}& = & -12 \color{red}{ +15x } \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9-15x } & = & -12 \color{red}{ +15x }\color{blue}{+9-15x } \\\Leftrightarrow & -x \color{blue}{-15x } & = & -12 \color{blue}{+9} \\\Leftrightarrow &-16x & = &-3\\\Leftrightarrow & \color{red}{-16}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{16} } & & \\ & V = \left\{ \frac{3}{16} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+11}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-x } & = & -8 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &-3x & = &-19\\\Leftrightarrow & \color{red}{-3}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-19}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{19}{3} } & & \\ & V = \left\{ \frac{19}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{-1}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-1}\color{blue}{+1-x } & = & -12 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -12 \color{blue}{+1} \\\Leftrightarrow &-7x & = &-11\\\Leftrightarrow & \color{red}{-7}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-11}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-8}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8-7x } & = & -10 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & -10 \color{blue}{+8} \\\Leftrightarrow &-5x & = &-2\\\Leftrightarrow & \color{red}{-5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-3}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3-7x } & = & -2 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & -2 \color{blue}{+3} \\\Leftrightarrow &5x & = &1\\\Leftrightarrow & \color{red}{5}x & = &1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+12}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12-5x } & = & 10 \color{red}{ +5x }\color{blue}{-12-5x } \\\Leftrightarrow & 13x \color{blue}{-5x } & = & 10 \color{blue}{-12} \\\Leftrightarrow &8x & = &-2\\\Leftrightarrow & \color{red}{8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-9}& = & -8 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{-9}\color{blue}{+9+10x } & = & -8 \color{red}{ -10x }\color{blue}{+9+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &21x & = &1\\\Leftrightarrow & \color{red}{21}x & = &1\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{1}{21} \\\Leftrightarrow & \color{green}{ x = \frac{1}{21} } & & \\ & V = \left\{ \frac{1}{21} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-11}& = & 15 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-3x } & = & 15 \color{red}{ +3x }\color{blue}{+11-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 15 \color{blue}{+11} \\\Leftrightarrow &-8x & = &26\\\Leftrightarrow & \color{red}{-8}x & = &26\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{26}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{4} } & & \\ & V = \left\{ \frac{-13}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{-3}& = & 9 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{-3}\color{blue}{+3-3x } & = & 9 \color{red}{ +3x }\color{blue}{+3-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & 9 \color{blue}{+3} \\\Leftrightarrow &5x & = &12\\\Leftrightarrow & \color{red}{5}x & = &12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-3}& = & 1 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3-4x } & = & 1 \color{red}{ +4x }\color{blue}{+3-4x } \\\Leftrightarrow & 11x \color{blue}{-4x } & = & 1 \color{blue}{+3} \\\Leftrightarrow &7x & = &4\\\Leftrightarrow & \color{red}{7}x & = &4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)