Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-9}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-9}\color{blue}{+9-x } & = & -10 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -10 \color{blue}{+9} \\\Leftrightarrow &-8x & = &-1\\\Leftrightarrow & \color{red}{-8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-8}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-8}\color{blue}{+8-x } & = & -2 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -2 \color{blue}{+8} \\\Leftrightarrow &-9x & = &6\\\Leftrightarrow & \color{red}{-9}x & = &6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{+12}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12-x } & = & -15 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -15 \color{blue}{-12} \\\Leftrightarrow &x & = &-27\\\Leftrightarrow & \color{red}{}x & = &-27\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -27 \\\Leftrightarrow & \color{green}{ x = -27 } & & \\ & V = \left\{ -27 \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-12}& = & -12 \color{red}{ +6x } \\\Leftrightarrow & 13x \color{red}{-12}\color{blue}{+12-6x } & = & -12 \color{red}{ +6x }\color{blue}{+12-6x } \\\Leftrightarrow & 13x \color{blue}{-6x } & = & -12 \color{blue}{+12} \\\Leftrightarrow &7x & = &0\\\Leftrightarrow & \color{red}{7}x & = &0\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{0}{7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+5}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+5}\color{blue}{-5-x } & = & -1 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -1 \color{blue}{-5} \\\Leftrightarrow &-13x & = &-6\\\Leftrightarrow & \color{red}{-13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-9}& = & -2 \color{red}{ -11x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9+11x } & = & -2 \color{red}{ -11x }\color{blue}{+9+11x } \\\Leftrightarrow & x \color{blue}{+11x } & = & -2 \color{blue}{+9} \\\Leftrightarrow &12x & = &7\\\Leftrightarrow & \color{red}{12}x & = &7\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{7}{12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-7}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{-7}\color{blue}{+7-13x } & = & -7 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &-18x & = &0\\\Leftrightarrow & \color{red}{-18}x & = &0\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{0}{-18} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-12}& = & 11 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12+10x } & = & 11 \color{red}{ -10x }\color{blue}{+12+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 11 \color{blue}{+12} \\\Leftrightarrow &21x & = &23\\\Leftrightarrow & \color{red}{21}x & = &23\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{23}{21} \\\Leftrightarrow & \color{green}{ x = \frac{23}{21} } & & \\ & V = \left\{ \frac{23}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+6}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{+6}\color{blue}{-6-7x } & = & -3 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & -3 \color{blue}{-6} \\\Leftrightarrow &-x & = &-9\\\Leftrightarrow & \color{red}{-}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-9}{-1} \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-11}& = & -6 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-11}\color{blue}{+11+9x } & = & -6 \color{red}{ -9x }\color{blue}{+11+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & -6 \color{blue}{+11} \\\Leftrightarrow &19x & = &5\\\Leftrightarrow & \color{red}{19}x & = &5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{5}{19} } & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{-1}& = & 8 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-1}\color{blue}{+1+14x } & = & 8 \color{red}{ -14x }\color{blue}{+1+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 8 \color{blue}{+1} \\\Leftrightarrow &29x & = &9\\\Leftrightarrow & \color{red}{29}x & = &9\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{9}{29} \\\Leftrightarrow & \color{green}{ x = \frac{9}{29} } & & \\ & V = \left\{ \frac{9}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{-2}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & -8x \color{red}{-2}\color{blue}{+2-11x } & = & 4 \color{red}{ +11x }\color{blue}{+2-11x } \\\Leftrightarrow & -8x \color{blue}{-11x } & = & 4 \color{blue}{+2} \\\Leftrightarrow &-19x & = &6\\\Leftrightarrow & \color{red}{-19}x & = &6\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{6}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{19} } & & \\ & V = \left\{ \frac{-6}{19} \right\} & \\\end{align}\)