Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+6}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6-x } & = & -11 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -11 \color{blue}{-6} \\\Leftrightarrow &-9x & = &-17\\\Leftrightarrow & \color{red}{-9}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-17}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{17}{9} } & & \\ & V = \left\{ \frac{17}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{-7}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7-x } & = & 2 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 2 \color{blue}{+7} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-5}& = & 9 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-3x } & = & 9 \color{red}{ +3x }\color{blue}{+5-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & 9 \color{blue}{+5} \\\Leftrightarrow &-x & = &14\\\Leftrightarrow & \color{red}{-}x & = &14\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{14}{-1} \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+11}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11-11x } & = & 4 \color{red}{ +11x }\color{blue}{-11-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 4 \color{blue}{-11} \\\Leftrightarrow &x & = &-7\\\Leftrightarrow & \color{red}{}x & = &-7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -7 \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-7}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-7}\color{blue}{+7-x } & = & -12 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -12 \color{blue}{+7} \\\Leftrightarrow &-13x & = &-5\\\Leftrightarrow & \color{red}{-13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-12}& = & -11 \color{red}{ +9x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12-9x } & = & -11 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & -x \color{blue}{-9x } & = & -11 \color{blue}{+12} \\\Leftrightarrow &-10x & = &1\\\Leftrightarrow & \color{red}{-10}x & = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+11}& = & -11 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11-8x } & = & -11 \color{red}{ +8x }\color{blue}{-11-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -11 \color{blue}{-11} \\\Leftrightarrow &-23x & = &-22\\\Leftrightarrow & \color{red}{-23}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-22}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{22}{23} } & & \\ & V = \left\{ \frac{22}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+9}& = & -15 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{+9}\color{blue}{-9-12x } & = & -15 \color{red}{ +12x }\color{blue}{-9-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & -15 \color{blue}{-9} \\\Leftrightarrow &-23x & = &-24\\\Leftrightarrow & \color{red}{-23}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-24}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{24}{23} } & & \\ & V = \left\{ \frac{24}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{+1}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1-x } & = & 6 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &-15x & = &5\\\Leftrightarrow & \color{red}{-15}x & = &5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{+4}& = & 7 \color{red}{ -9x } \\\Leftrightarrow & x \color{red}{+4}\color{blue}{-4+9x } & = & 7 \color{red}{ -9x }\color{blue}{-4+9x } \\\Leftrightarrow & x \color{blue}{+9x } & = & 7 \color{blue}{-4} \\\Leftrightarrow &10x & = &3\\\Leftrightarrow & \color{red}{10}x & = &3\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{3}{10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{10} } & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-4}& = & 8 \color{red}{ +11x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4-11x } & = & 8 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & 13x \color{blue}{-11x } & = & 8 \color{blue}{+4} \\\Leftrightarrow &2x & = &12\\\Leftrightarrow & \color{red}{2}x & = &12\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{12}{2} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+4}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{+4}\color{blue}{-4-13x } & = & 5 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & 5 \color{blue}{-4} \\\Leftrightarrow &-9x & = &1\\\Leftrightarrow & \color{red}{-9}x & = &1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)