Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+7}& = & 5 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+7}\color{blue}{-7-8x } & = & 5 \color{red}{ +8x }\color{blue}{-7-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & 5 \color{blue}{-7} \\\Leftrightarrow &-23x & = &-2\\\Leftrightarrow & \color{red}{-23}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-2}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{2}{23} } & & \\ & V = \left\{ \frac{2}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{+11}& = & 9 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{+11}\color{blue}{-11-8x } & = & 9 \color{red}{ +8x }\color{blue}{-11-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & 9 \color{blue}{-11} \\\Leftrightarrow &-x & = &-2\\\Leftrightarrow & \color{red}{-}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-2}{-1} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-5}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5-13x } & = & -1 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & -1 \color{blue}{+5} \\\Leftrightarrow &-7x & = &4\\\Leftrightarrow & \color{red}{-7}x & = &4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+3}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3-x } & = & 7 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 7 \color{blue}{-3} \\\Leftrightarrow &-11x & = &4\\\Leftrightarrow & \color{red}{-11}x & = &4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+6}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6-x } & = & 9 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 9 \color{blue}{-6} \\\Leftrightarrow &-9x & = &3\\\Leftrightarrow & \color{red}{-9}x & = &3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+11}& = & -14 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11+15x } & = & -14 \color{red}{ -15x }\color{blue}{-11+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &23x & = &-25\\\Leftrightarrow & \color{red}{23}x & = &-25\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-25}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{23} } & & \\ & V = \left\{ \frac{-25}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+3}& = & -1 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+3}\color{blue}{-3+4x } & = & -1 \color{red}{ -4x }\color{blue}{-3+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -1 \color{blue}{-3} \\\Leftrightarrow &9x & = &-4\\\Leftrightarrow & \color{red}{9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+4}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+4}\color{blue}{-4-x } & = & -15 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -15 \color{blue}{-4} \\\Leftrightarrow &-15x & = &-19\\\Leftrightarrow & \color{red}{-15}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-19}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{19}{15} } & & \\ & V = \left\{ \frac{19}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+7}& = & 3 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+7}\color{blue}{-7-14x } & = & 3 \color{red}{ +14x }\color{blue}{-7-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 3 \color{blue}{-7} \\\Leftrightarrow &-25x & = &-4\\\Leftrightarrow & \color{red}{-25}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-4}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{4}{25} } & & \\ & V = \left\{ \frac{4}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{+15}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15+11x } & = & 11 \color{red}{ -11x }\color{blue}{-15+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 11 \color{blue}{-15} \\\Leftrightarrow &15x & = &-4\\\Leftrightarrow & \color{red}{15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-4}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+10}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+10}\color{blue}{-10-x } & = & 11 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 11 \color{blue}{-10} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{-12}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12-x } & = & 4 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 4 \color{blue}{+12} \\\Leftrightarrow &-3x & = &16\\\Leftrightarrow & \color{red}{-3}x & = &16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)