Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{-4}& = & 12 \color{red}{ +3x } \\\Leftrightarrow & x \color{red}{-4}\color{blue}{+4-3x } & = & 12 \color{red}{ +3x }\color{blue}{+4-3x } \\\Leftrightarrow & x \color{blue}{-3x } & = & 12 \color{blue}{+4} \\\Leftrightarrow &-2x & = &16\\\Leftrightarrow & \color{red}{-2}x & = &16\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{16}{-2} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{-13}& = & 5 \color{red}{ +9x } \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13-9x } & = & 5 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & 5x \color{blue}{-9x } & = & 5 \color{blue}{+13} \\\Leftrightarrow &-4x & = &18\\\Leftrightarrow & \color{red}{-4}x & = &18\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{18}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{-6}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-6}\color{blue}{+6-7x } & = & 4 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 4 \color{blue}{+6} \\\Leftrightarrow &-17x & = &10\\\Leftrightarrow & \color{red}{-17}x & = &10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-13}& = & 15 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-13}\color{blue}{+13+2x } & = & 15 \color{red}{ -2x }\color{blue}{+13+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 15 \color{blue}{+13} \\\Leftrightarrow &17x & = &28\\\Leftrightarrow & \color{red}{17}x & = &28\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{28}{17} \\\Leftrightarrow & \color{green}{ x = \frac{28}{17} } & & \\ & V = \left\{ \frac{28}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-9}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-x } & = & -11 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -11 \color{blue}{+9} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+4}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4-7x } & = & 11 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 11 \color{blue}{-4} \\\Leftrightarrow &-17x & = &7\\\Leftrightarrow & \color{red}{-17}x & = &7\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{7}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{17} } & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-4}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-4}\color{blue}{+4-x } & = & 1 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 1 \color{blue}{+4} \\\Leftrightarrow &-4x & = &5\\\Leftrightarrow & \color{red}{-4}x & = &5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+9}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+9}\color{blue}{-9-x } & = & -1 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -1 \color{blue}{-9} \\\Leftrightarrow &-9x & = &-10\\\Leftrightarrow & \color{red}{-9}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{10}{9} } & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-13}& = & -2 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-13}\color{blue}{+13+14x } & = & -2 \color{red}{ -14x }\color{blue}{+13+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & -2 \color{blue}{+13} \\\Leftrightarrow &29x & = &11\\\Leftrightarrow & \color{red}{29}x & = &11\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{11}{29} \\\Leftrightarrow & \color{green}{ x = \frac{11}{29} } & & \\ & V = \left\{ \frac{11}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-4}& = & -7 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-4}\color{blue}{+4-3x } & = & -7 \color{red}{ +3x }\color{blue}{+4-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & -7 \color{blue}{+4} \\\Leftrightarrow &-x & = &-3\\\Leftrightarrow & \color{red}{-}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-3}{-1} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-9}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-9}\color{blue}{+9-x } & = & 7 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 7 \color{blue}{+9} \\\Leftrightarrow &-16x & = &16\\\Leftrightarrow & \color{red}{-16}x & = &16\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{16}{-16} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{+4}& = & -12 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4+7x } & = & -12 \color{red}{ -7x }\color{blue}{-4+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -12 \color{blue}{-4} \\\Leftrightarrow &19x & = &-16\\\Leftrightarrow & \color{red}{19}x & = &-16\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-16}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{19} } & & \\ & V = \left\{ \frac{-16}{19} \right\} & \\\end{align}\)