Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-6}& = & 13 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-4x } & = & 13 \color{red}{ +4x }\color{blue}{+6-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & 13 \color{blue}{+6} \\\Leftrightarrow &-7x & = &19\\\Leftrightarrow & \color{red}{-7}x & = &19\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{19}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{7} } & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+9}& = & -10 \color{red}{ -13x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9+13x } & = & -10 \color{red}{ -13x }\color{blue}{-9+13x } \\\Leftrightarrow & x \color{blue}{+13x } & = & -10 \color{blue}{-9} \\\Leftrightarrow &14x & = &-19\\\Leftrightarrow & \color{red}{14}x & = &-19\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-19}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{14} } & & \\ & V = \left\{ \frac{-19}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{-4}& = & -2 \color{red}{ -4x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4+4x } & = & -2 \color{red}{ -4x }\color{blue}{+4+4x } \\\Leftrightarrow & 13x \color{blue}{+4x } & = & -2 \color{blue}{+4} \\\Leftrightarrow &17x & = &2\\\Leftrightarrow & \color{red}{17}x & = &2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-13}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-13}\color{blue}{+13-x } & = & 6 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 6 \color{blue}{+13} \\\Leftrightarrow &-13x & = &19\\\Leftrightarrow & \color{red}{-13}x & = &19\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{19}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-9}& = & 10 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-9}\color{blue}{+9+6x } & = & 10 \color{red}{ -6x }\color{blue}{+9+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 10 \color{blue}{+9} \\\Leftrightarrow &19x & = &19\\\Leftrightarrow & \color{red}{19}x & = &19\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{19}{19} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+6}& = & -12 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6+13x } & = & -12 \color{red}{ -13x }\color{blue}{-6+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -12 \color{blue}{-6} \\\Leftrightarrow &23x & = &-18\\\Leftrightarrow & \color{red}{23}x & = &-18\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-18}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{23} } & & \\ & V = \left\{ \frac{-18}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+15}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+15}\color{blue}{-15-5x } & = & -2 \color{red}{ +5x }\color{blue}{-15-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -2 \color{blue}{-15} \\\Leftrightarrow &7x & = &-17\\\Leftrightarrow & \color{red}{7}x & = &-17\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-17}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{7} } & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-12}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12-7x } & = & -7 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -7 \color{blue}{+12} \\\Leftrightarrow &-20x & = &5\\\Leftrightarrow & \color{red}{-20}x & = &5\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{5}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+11}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11-x } & = & 12 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 12 \color{blue}{-11} \\\Leftrightarrow &-16x & = &1\\\Leftrightarrow & \color{red}{-16}x & = &1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{16} } & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-3}& = & -13 \color{red}{ +2x } \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3-2x } & = & -13 \color{red}{ +2x }\color{blue}{+3-2x } \\\Leftrightarrow & 11x \color{blue}{-2x } & = & -13 \color{blue}{+3} \\\Leftrightarrow &9x & = &-10\\\Leftrightarrow & \color{red}{9}x & = &-10\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-10}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+9}& = & -1 \color{red}{ +12x } \\\Leftrightarrow & 13x \color{red}{+9}\color{blue}{-9-12x } & = & -1 \color{red}{ +12x }\color{blue}{-9-12x } \\\Leftrightarrow & 13x \color{blue}{-12x } & = & -1 \color{blue}{-9} \\\Leftrightarrow &x & = &-10\\\Leftrightarrow & \color{red}{}x & = &-10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -10 \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+4}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x } & = & -3 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -3 \color{blue}{-4} \\\Leftrightarrow &-14x & = &-7\\\Leftrightarrow & \color{red}{-14}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-7}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)