Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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