Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{-10}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{-10}\color{blue}{+10-x } & = & 7 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 7 \color{blue}{+10} \\\Leftrightarrow &12x & = &17\\\Leftrightarrow & \color{red}{12}x & = &17\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{17}{12} \\\Leftrightarrow & \color{green}{ x = \frac{17}{12} } & & \\ & V = \left\{ \frac{17}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{-5}& = & 15 \color{red}{ +4x } \\\Leftrightarrow & -11x \color{red}{-5}\color{blue}{+5-4x } & = & 15 \color{red}{ +4x }\color{blue}{+5-4x } \\\Leftrightarrow & -11x \color{blue}{-4x } & = & 15 \color{blue}{+5} \\\Leftrightarrow &-15x & = &20\\\Leftrightarrow & \color{red}{-15}x & = &20\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{20}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+15}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+15}\color{blue}{-15-13x } & = & 12 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 12 \color{blue}{-15} \\\Leftrightarrow &-25x & = &-3\\\Leftrightarrow & \color{red}{-25}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-3}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{3}{25} } & & \\ & V = \left\{ \frac{3}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+1}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+1}\color{blue}{-1-x } & = & -14 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -14 \color{blue}{-1} \\\Leftrightarrow &-11x & = &-15\\\Leftrightarrow & \color{red}{-11}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{15}{11} } & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-10}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-10}\color{blue}{+10-x } & = & 11 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 11 \color{blue}{+10} \\\Leftrightarrow &-6x & = &21\\\Leftrightarrow & \color{red}{-6}x & = &21\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{21}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+10}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+10}\color{blue}{-10-x } & = & 2 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 2 \color{blue}{-10} \\\Leftrightarrow &-14x & = &-8\\\Leftrightarrow & \color{red}{-14}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{-13}& = & 9 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-13}\color{blue}{+13-14x } & = & 9 \color{red}{ +14x }\color{blue}{+13-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 9 \color{blue}{+13} \\\Leftrightarrow &-23x & = &22\\\Leftrightarrow & \color{red}{-23}x & = &22\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{22}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{23} } & & \\ & V = \left\{ \frac{-22}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+8}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{+8}\color{blue}{-8-x } & = & 14 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & 14 \color{blue}{-8} \\\Leftrightarrow &4x & = &6\\\Leftrightarrow & \color{red}{4}x & = &6\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{6}{4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{-9}& = & -5 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-9}\color{blue}{+9-3x } & = & -5 \color{red}{ +3x }\color{blue}{+9-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & -5 \color{blue}{+9} \\\Leftrightarrow &-x & = &4\\\Leftrightarrow & \color{red}{-}x & = &4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{4}{-1} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-8}& = & 8 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8-4x } & = & 8 \color{red}{ +4x }\color{blue}{+8-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & 8 \color{blue}{+8} \\\Leftrightarrow &-11x & = &16\\\Leftrightarrow & \color{red}{-11}x & = &16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{-14}& = & -10 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14+5x } & = & -10 \color{red}{ -5x }\color{blue}{+14+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & -10 \color{blue}{+14} \\\Leftrightarrow &16x & = &4\\\Leftrightarrow & \color{red}{16}x & = &4\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{4}{16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+3}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+3}\color{blue}{-3-x } & = & 13 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 13 \color{blue}{-3} \\\Leftrightarrow &x & = &10\\\Leftrightarrow & \color{red}{}x & = &10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 10 \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)