Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-10}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10-x } & = & -15 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -15 \color{blue}{+10} \\\Leftrightarrow &-8x & = &-5\\\Leftrightarrow & \color{red}{-8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{-2}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-2}\color{blue}{+2-x } & = & -15 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -15 \color{blue}{+2} \\\Leftrightarrow &x & = &-13\\\Leftrightarrow & \color{red}{}x & = &-13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -13 \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-7}& = & 10 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-7}\color{blue}{+7+14x } & = & 10 \color{red}{ -14x }\color{blue}{+7+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 10 \color{blue}{+7} \\\Leftrightarrow &29x & = &17\\\Leftrightarrow & \color{red}{29}x & = &17\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{17}{29} \\\Leftrightarrow & \color{green}{ x = \frac{17}{29} } & & \\ & V = \left\{ \frac{17}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-2}& = & -13 \color{red}{ +11x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2-11x } & = & -13 \color{red}{ +11x }\color{blue}{+2-11x } \\\Leftrightarrow & 9x \color{blue}{-11x } & = & -13 \color{blue}{+2} \\\Leftrightarrow &-2x & = &-11\\\Leftrightarrow & \color{red}{-2}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-11}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-14}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14-x } & = & 13 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 13 \color{blue}{+14} \\\Leftrightarrow &-14x & = &27\\\Leftrightarrow & \color{red}{-14}x & = &27\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{27}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{14} } & & \\ & V = \left\{ \frac{-27}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-2}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-2}\color{blue}{+2-x } & = & -9 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -9 \color{blue}{+2} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{-9}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9-13x } & = & 3 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & 3 \color{blue}{+9} \\\Leftrightarrow &-9x & = &12\\\Leftrightarrow & \color{red}{-9}x & = &12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+1}& = & -2 \color{red}{ -x } \\\Leftrightarrow & x \color{red}{+1}\color{blue}{-1+x } & = & -2 \color{red}{ -x }\color{blue}{-1+x } \\\Leftrightarrow & x \color{blue}{+x } & = & -2 \color{blue}{-1} \\\Leftrightarrow &2x & = &-3\\\Leftrightarrow & \color{red}{2}x & = &-3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{-1}& = & -8 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-1}\color{blue}{+1-9x } & = & -8 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -8 \color{blue}{+1} \\\Leftrightarrow &5x & = &-7\\\Leftrightarrow & \color{red}{5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+5}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-x } & = & 7 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 7 \color{blue}{-5} \\\Leftrightarrow &-6x & = &2\\\Leftrightarrow & \color{red}{-6}x & = &2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-9}& = & 14 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9+7x } & = & 14 \color{red}{ -7x }\color{blue}{+9+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 14 \color{blue}{+9} \\\Leftrightarrow &11x & = &23\\\Leftrightarrow & \color{red}{11}x & = &23\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{23}{11} \\\Leftrightarrow & \color{green}{ x = \frac{23}{11} } & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+10}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-x } & = & -9 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -9 \color{blue}{-10} \\\Leftrightarrow &-6x & = &-19\\\Leftrightarrow & \color{red}{-6}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-19}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{19}{6} } & & \\ & V = \left\{ \frac{19}{6} \right\} & \\\end{align}\)