Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+7}& = & -1 \color{red}{ +3x } \\\Leftrightarrow & -8x \color{red}{+7}\color{blue}{-7-3x } & = & -1 \color{red}{ +3x }\color{blue}{-7-3x } \\\Leftrightarrow & -8x \color{blue}{-3x } & = & -1 \color{blue}{-7} \\\Leftrightarrow &-11x & = &-8\\\Leftrightarrow & \color{red}{-11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-7}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-7}\color{blue}{+7-x } & = & 12 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 12 \color{blue}{+7} \\\Leftrightarrow &-5x & = &19\\\Leftrightarrow & \color{red}{-5}x & = &19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{5} } & & \\ & V = \left\{ \frac{-19}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{-11}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11-11x } & = & -14 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -14 \color{blue}{+11} \\\Leftrightarrow &-21x & = &-3\\\Leftrightarrow & \color{red}{-21}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-3}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-9}& = & 14 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-6x } & = & 14 \color{red}{ +6x }\color{blue}{+9-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 14 \color{blue}{+9} \\\Leftrightarrow &-11x & = &23\\\Leftrightarrow & \color{red}{-11}x & = &23\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{23}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{11} } & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+6}& = & -3 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6-3x } & = & -3 \color{red}{ +3x }\color{blue}{-6-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & -3 \color{blue}{-6} \\\Leftrightarrow &7x & = &-9\\\Leftrightarrow & \color{red}{7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-6}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-13x } & = & -2 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -2 \color{blue}{+6} \\\Leftrightarrow &-25x & = &4\\\Leftrightarrow & \color{red}{-25}x & = &4\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{4}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{25} } & & \\ & V = \left\{ \frac{-4}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+7}& = & -15 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7+12x } & = & -15 \color{red}{ -12x }\color{blue}{-7+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -15 \color{blue}{-7} \\\Leftrightarrow &25x & = &-22\\\Leftrightarrow & \color{red}{25}x & = &-22\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-22}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{25} } & & \\ & V = \left\{ \frac{-22}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+10}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+10}\color{blue}{-10-x } & = & 12 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 12 \color{blue}{-10} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-7}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-7x } & = & -14 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -14 \color{blue}{+7} \\\Leftrightarrow &-20x & = &-7\\\Leftrightarrow & \color{red}{-20}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-7}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{7}{20} } & & \\ & V = \left\{ \frac{7}{20} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+13}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+13}\color{blue}{-13-x } & = & -1 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -1 \color{blue}{-13} \\\Leftrightarrow &-8x & = &-14\\\Leftrightarrow & \color{red}{-8}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-14}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+7}& = & -12 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{+7}\color{blue}{-7-3x } & = & -12 \color{red}{ +3x }\color{blue}{-7-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &-14x & = &-19\\\Leftrightarrow & \color{red}{-14}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-19}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{19}{14} } & & \\ & V = \left\{ \frac{19}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-12}& = & -10 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12+13x } & = & -10 \color{red}{ -13x }\color{blue}{+12+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -10 \color{blue}{+12} \\\Leftrightarrow &24x & = &2\\\Leftrightarrow & \color{red}{24}x & = &2\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{2}{24} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)