Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{-2}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-2}\color{blue}{+2-x } & = & -2 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -2 \color{blue}{+2} \\\Leftrightarrow &-15x & = &0\\\Leftrightarrow & \color{red}{-15}x & = &0\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{0}{-15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+6}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6-13x } & = & -1 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -1 \color{blue}{-6} \\\Leftrightarrow &-28x & = &-7\\\Leftrightarrow & \color{red}{-28}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-7}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-9}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-13x } & = & 3 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & 3 \color{blue}{+9} \\\Leftrightarrow &-16x & = &12\\\Leftrightarrow & \color{red}{-16}x & = &12\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{12}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-8}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8-x } & = & 7 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 7 \color{blue}{+8} \\\Leftrightarrow &-5x & = &15\\\Leftrightarrow & \color{red}{-5}x & = &15\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{15}{-5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{+11}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11-7x } & = & 15 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -x \color{blue}{-7x } & = & 15 \color{blue}{-11} \\\Leftrightarrow &-8x & = &4\\\Leftrightarrow & \color{red}{-8}x & = &4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+11}& = & -11 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11-7x } & = & -11 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & -11 \color{blue}{-11} \\\Leftrightarrow &-4x & = &-22\\\Leftrightarrow & \color{red}{-4}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-22}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+4}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+4}\color{blue}{-4-x } & = & -12 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -12 \color{blue}{-4} \\\Leftrightarrow &-4x & = &-16\\\Leftrightarrow & \color{red}{-4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-16}{-4} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{-1}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1-x } & = & 2 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 2 \color{blue}{+1} \\\Leftrightarrow &-6x & = &3\\\Leftrightarrow & \color{red}{-6}x & = &3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-1}& = & 5 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-1}\color{blue}{+1+14x } & = & 5 \color{red}{ -14x }\color{blue}{+1+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & 5 \color{blue}{+1} \\\Leftrightarrow &19x & = &6\\\Leftrightarrow & \color{red}{19}x & = &6\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{6}{19} \\\Leftrightarrow & \color{green}{ x = \frac{6}{19} } & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-14}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14-7x } & = & -8 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -8 \color{blue}{+14} \\\Leftrightarrow &-20x & = &6\\\Leftrightarrow & \color{red}{-20}x & = &6\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{6}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{+14}& = & 10 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+14}\color{blue}{-14-9x } & = & 10 \color{red}{ +9x }\color{blue}{-14-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 10 \color{blue}{-14} \\\Leftrightarrow &-13x & = &-4\\\Leftrightarrow & \color{red}{-13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{+3}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3-13x } & = & 4 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & 4 \color{blue}{-3} \\\Leftrightarrow &-10x & = &1\\\Leftrightarrow & \color{red}{-10}x & = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)