Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{-8}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-8}\color{blue}{+8-9x } & = & -14 \color{red}{ +9x }\color{blue}{+8-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -14 \color{blue}{+8} \\\Leftrightarrow &-17x & = &-6\\\Leftrightarrow & \color{red}{-17}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-6}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{6}{17} } & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{-12}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-x } & = & 5 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 5 \color{blue}{+12} \\\Leftrightarrow &-6x & = &17\\\Leftrightarrow & \color{red}{-6}x & = &17\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{17}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{6} } & & \\ & V = \left\{ \frac{-17}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{+3}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{+3}\color{blue}{-3-13x } & = & 11 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & 11 \color{blue}{-3} \\\Leftrightarrow &-11x & = &8\\\Leftrightarrow & \color{red}{-11}x & = &8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+3}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3-x } & = & -13 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -13 \color{blue}{-3} \\\Leftrightarrow &-7x & = &-16\\\Leftrightarrow & \color{red}{-7}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{16}{7} } & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+15}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+15}\color{blue}{-15+11x } & = & 11 \color{red}{ -11x }\color{blue}{-15+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 11 \color{blue}{-15} \\\Leftrightarrow &23x & = &-4\\\Leftrightarrow & \color{red}{23}x & = &-4\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-4}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{23} } & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2-x } & = & -3 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &8x & = &-5\\\Leftrightarrow & \color{red}{8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-5}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{-1}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1-13x } & = & 10 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 10 \color{blue}{+1} \\\Leftrightarrow &-28x & = &11\\\Leftrightarrow & \color{red}{-28}x & = &11\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{11}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{28} } & & \\ & V = \left\{ \frac{-11}{28} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-10}& = & 5 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{-10}\color{blue}{+10-7x } & = & 5 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & 5 \color{blue}{+10} \\\Leftrightarrow &-3x & = &15\\\Leftrightarrow & \color{red}{-3}x & = &15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{15}{-3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{+11}& = & -12 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11-5x } & = & -12 \color{red}{ +5x }\color{blue}{-11-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & -12 \color{blue}{-11} \\\Leftrightarrow &-x & = &-23\\\Leftrightarrow & \color{red}{-}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-23}{-1} \\\Leftrightarrow & \color{green}{ x = 23 } & & \\ & V = \left\{ 23 \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2-x } & = & 4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &-10x & = &2\\\Leftrightarrow & \color{red}{-10}x & = &2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+1}& = & -12 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1+7x } & = & -12 \color{red}{ -7x }\color{blue}{-1+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & -12 \color{blue}{-1} \\\Leftrightarrow &12x & = &-13\\\Leftrightarrow & \color{red}{12}x & = &-13\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-13}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{12} } & & \\ & V = \left\{ \frac{-13}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{+4}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-x } & = & -14 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &-13x & = &-18\\\Leftrightarrow & \color{red}{-13}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-18}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{18}{13} } & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)