Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+14}& = & 1 \color{red}{ +10x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-10x } & = & 1 \color{red}{ +10x }\color{blue}{-14-10x } \\\Leftrightarrow & -13x \color{blue}{-10x } & = & 1 \color{blue}{-14} \\\Leftrightarrow &-23x & = &-13\\\Leftrightarrow & \color{red}{-23}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-13}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{13}{23} } & & \\ & V = \left\{ \frac{13}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+8}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{+8}\color{blue}{-8-x } & = & 1 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & 1 \color{blue}{-8} \\\Leftrightarrow &4x & = &-7\\\Leftrightarrow & \color{red}{4}x & = &-7\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-7}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{+1}& = & 12 \color{red}{ +5x } \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1-5x } & = & 12 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & -x \color{blue}{-5x } & = & 12 \color{blue}{-1} \\\Leftrightarrow &-6x & = &11\\\Leftrightarrow & \color{red}{-6}x & = &11\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{11}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+7}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7-5x } & = & 11 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 11 \color{blue}{-7} \\\Leftrightarrow &x & = &4\\\Leftrightarrow & \color{red}{}x & = &4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 4 \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-10}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-10}\color{blue}{+10-x } & = & 12 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 12 \color{blue}{+10} \\\Leftrightarrow &-4x & = &22\\\Leftrightarrow & \color{red}{-4}x & = &22\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{22}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{2} } & & \\ & V = \left\{ \frac{-11}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+6}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6-x } & = & 4 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 4 \color{blue}{-6} \\\Leftrightarrow &-3x & = &-2\\\Leftrightarrow & \color{red}{-3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{+8}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8-x } & = & -12 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & -12 \color{blue}{-8} \\\Leftrightarrow &10x & = &-20\\\Leftrightarrow & \color{red}{10}x & = &-20\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-20}{10} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+1}& = & -8 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+1}\color{blue}{-1-9x } & = & -8 \color{red}{ +9x }\color{blue}{-1-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -8 \color{blue}{-1} \\\Leftrightarrow &-17x & = &-9\\\Leftrightarrow & \color{red}{-17}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-9}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{9}{17} } & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-1}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1-13x } & = & -1 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & -1 \color{blue}{+1} \\\Leftrightarrow &-x & = &0\\\Leftrightarrow & \color{red}{-}x & = &0\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{0}{-1} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-12}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12+11x } & = & 7 \color{red}{ -11x }\color{blue}{+12+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 7 \color{blue}{+12} \\\Leftrightarrow &23x & = &19\\\Leftrightarrow & \color{red}{23}x & = &19\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{19}{23} \\\Leftrightarrow & \color{green}{ x = \frac{19}{23} } & & \\ & V = \left\{ \frac{19}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+1}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1-7x } & = & 11 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & 11 \color{blue}{-1} \\\Leftrightarrow &8x & = &10\\\Leftrightarrow & \color{red}{8}x & = &10\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{10}{8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-10}& = & -11 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-10}\color{blue}{+10-7x } & = & -11 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -11 \color{blue}{+10} \\\Leftrightarrow &8x & = &-1\\\Leftrightarrow & \color{red}{8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)