Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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