Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-8}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-8}\color{blue}{+8-x } & = & -15 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -15 \color{blue}{+8} \\\Leftrightarrow &-10x & = &-7\\\Leftrightarrow & \color{red}{-10}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{-8}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8-x } & = & 10 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 10 \color{blue}{+8} \\\Leftrightarrow &-8x & = &18\\\Leftrightarrow & \color{red}{-8}x & = &18\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{18}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+13}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+13}\color{blue}{-13-x } & = & 13 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 13 \color{blue}{-13} \\\Leftrightarrow &-15x & = &0\\\Leftrightarrow & \color{red}{-15}x & = &0\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{0}{-15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+4}& = & 12 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+4}\color{blue}{-4+10x } & = & 12 \color{red}{ -10x }\color{blue}{-4+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 12 \color{blue}{-4} \\\Leftrightarrow &21x & = &8\\\Leftrightarrow & \color{red}{21}x & = &8\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{8}{21} \\\Leftrightarrow & \color{green}{ x = \frac{8}{21} } & & \\ & V = \left\{ \frac{8}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{-8}& = & 15 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{-8}\color{blue}{+8-14x } & = & 15 \color{red}{ +14x }\color{blue}{+8-14x } \\\Leftrightarrow & 15x \color{blue}{-14x } & = & 15 \color{blue}{+8} \\\Leftrightarrow &x & = &23\\\Leftrightarrow & \color{red}{}x & = &23\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 23 \\\Leftrightarrow & \color{green}{ x = 23 } & & \\ & V = \left\{ 23 \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+12}& = & 2 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-11x } & = & 2 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & 2 \color{blue}{-12} \\\Leftrightarrow &-13x & = &-10\\\Leftrightarrow & \color{red}{-13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-11}& = & -5 \color{red}{ +14x } \\\Leftrightarrow & 5x \color{red}{-11}\color{blue}{+11-14x } & = & -5 \color{red}{ +14x }\color{blue}{+11-14x } \\\Leftrightarrow & 5x \color{blue}{-14x } & = & -5 \color{blue}{+11} \\\Leftrightarrow &-9x & = &6\\\Leftrightarrow & \color{red}{-9}x & = &6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{+6}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-x } & = & 2 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 2 \color{blue}{-6} \\\Leftrightarrow &-6x & = &-4\\\Leftrightarrow & \color{red}{-6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+1}& = & -7 \color{red}{ +9x } \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1-9x } & = & -7 \color{red}{ +9x }\color{blue}{-1-9x } \\\Leftrightarrow & -x \color{blue}{-9x } & = & -7 \color{blue}{-1} \\\Leftrightarrow &-10x & = &-8\\\Leftrightarrow & \color{red}{-10}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{+4}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x } & = & 9 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 9 \color{blue}{-4} \\\Leftrightarrow &-14x & = &5\\\Leftrightarrow & \color{red}{-14}x & = &5\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{5}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{14} } & & \\ & V = \left\{ \frac{-5}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-1}& = & 8 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{-1}\color{blue}{+1-3x } & = & 8 \color{red}{ +3x }\color{blue}{+1-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & 8 \color{blue}{+1} \\\Leftrightarrow &11x & = &9\\\Leftrightarrow & \color{red}{11}x & = &9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{-15}& = & -14 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-15}\color{blue}{+15+13x } & = & -14 \color{red}{ -13x }\color{blue}{+15+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -14 \color{blue}{+15} \\\Leftrightarrow &23x & = &1\\\Leftrightarrow & \color{red}{23}x & = &1\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{1}{23} \\\Leftrightarrow & \color{green}{ x = \frac{1}{23} } & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)