Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-5}& = & -5 \color{red}{ +3x } \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5-3x } & = & -5 \color{red}{ +3x }\color{blue}{+5-3x } \\\Leftrightarrow & -x \color{blue}{-3x } & = & -5 \color{blue}{+5} \\\Leftrightarrow &-4x & = &0\\\Leftrightarrow & \color{red}{-4}x & = &0\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{0}{-4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+12}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12-x } & = & 15 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 15 \color{blue}{-12} \\\Leftrightarrow &x & = &3\\\Leftrightarrow & \color{red}{}x & = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+2}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+2}\color{blue}{-2-x } & = & -4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -4 \color{blue}{-2} \\\Leftrightarrow &-9x & = &-6\\\Leftrightarrow & \color{red}{-9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-10}& = & -9 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-10}\color{blue}{+10-6x } & = & -9 \color{red}{ +6x }\color{blue}{+10-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -9 \color{blue}{+10} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+9}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9-5x } & = & -8 \color{red}{ +5x }\color{blue}{-9-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -8 \color{blue}{-9} \\\Leftrightarrow &x & = &-17\\\Leftrightarrow & \color{red}{}x & = &-17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -17 \\\Leftrightarrow & \color{green}{ x = -17 } & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{-1}& = & 2 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{-1}\color{blue}{+1+14x } & = & 2 \color{red}{ -14x }\color{blue}{+1+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & 2 \color{blue}{+1} \\\Leftrightarrow &17x & = &3\\\Leftrightarrow & \color{red}{17}x & = &3\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{3}{17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-3}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3-7x } & = & -3 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & 11x \color{blue}{-7x } & = & -3 \color{blue}{+3} \\\Leftrightarrow &4x & = &0\\\Leftrightarrow & \color{red}{4}x & = &0\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{0}{4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{-12}& = & -11 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-12}\color{blue}{+12+12x } & = & -11 \color{red}{ -12x }\color{blue}{+12+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -11 \color{blue}{+12} \\\Leftrightarrow &25x & = &1\\\Leftrightarrow & \color{red}{25}x & = &1\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{1}{25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{25} } & & \\ & V = \left\{ \frac{1}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-11}& = & -5 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-3x } & = & -5 \color{red}{ +3x }\color{blue}{+11-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & -5 \color{blue}{+11} \\\Leftrightarrow &-17x & = &6\\\Leftrightarrow & \color{red}{-17}x & = &6\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{6}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{17} } & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-9}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-x } & = & -3 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -3 \color{blue}{+9} \\\Leftrightarrow &-6x & = &6\\\Leftrightarrow & \color{red}{-6}x & = &6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{6}{-6} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-11}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11-7x } & = & -7 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -7 \color{blue}{+11} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{+1}& = & 13 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+1}\color{blue}{-1-11x } & = & 13 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &x & = &12\\\Leftrightarrow & \color{red}{}x & = &12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 12 \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)