Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{-4}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-4}\color{blue}{+4-x } & = & -5 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -5 \color{blue}{+4} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+8}& = & 3 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+8}\color{blue}{-8+11x } & = & 3 \color{red}{ -11x }\color{blue}{-8+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 3 \color{blue}{-8} \\\Leftrightarrow &23x & = &-5\\\Leftrightarrow & \color{red}{23}x & = &-5\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-5}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{23} } & & \\ & V = \left\{ \frac{-5}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{+3}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3-x } & = & -10 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -10 \color{blue}{-3} \\\Leftrightarrow &-7x & = &-13\\\Leftrightarrow & \color{red}{-7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-13}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{-11}& = & -1 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-11}\color{blue}{+11+7x } & = & -1 \color{red}{ -7x }\color{blue}{+11+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -1 \color{blue}{+11} \\\Leftrightarrow &11x & = &10\\\Leftrightarrow & \color{red}{11}x & = &10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-15}& = & 12 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{-15}\color{blue}{+15+9x } & = & 12 \color{red}{ -9x }\color{blue}{+15+9x } \\\Leftrightarrow & -x \color{blue}{+9x } & = & 12 \color{blue}{+15} \\\Leftrightarrow &8x & = &27\\\Leftrightarrow & \color{red}{8}x & = &27\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{27}{8} \\\Leftrightarrow & \color{green}{ x = \frac{27}{8} } & & \\ & V = \left\{ \frac{27}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+14}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14-x } & = & 13 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 13 \color{blue}{-14} \\\Leftrightarrow &5x & = &-1\\\Leftrightarrow & \color{red}{5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-5}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-5}\color{blue}{+5-x } & = & -3 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -3 \color{blue}{+5} \\\Leftrightarrow &-11x & = &2\\\Leftrightarrow & \color{red}{-11}x & = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{+2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+2}\color{blue}{-2-x } & = & -3 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &-14x & = &-5\\\Leftrightarrow & \color{red}{-14}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-5}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{14} } & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-15}& = & 10 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15+3x } & = & 10 \color{red}{ -3x }\color{blue}{+15+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 10 \color{blue}{+15} \\\Leftrightarrow &10x & = &25\\\Leftrightarrow & \color{red}{10}x & = &25\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{25}{10} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+1}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+1}\color{blue}{-1-x } & = & 13 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &11x & = &12\\\Leftrightarrow & \color{red}{11}x & = &12\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{12}{11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{-3}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-x } & = & -5 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -5 \color{blue}{+3} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{+3}& = & 9 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-10x } & = & 9 \color{red}{ +10x }\color{blue}{-3-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 9 \color{blue}{-3} \\\Leftrightarrow &-13x & = &6\\\Leftrightarrow & \color{red}{-13}x & = &6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)