Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-8}& = & 1 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{-8}\color{blue}{+8-10x } & = & 1 \color{red}{ +10x }\color{blue}{+8-10x } \\\Leftrightarrow & 3x \color{blue}{-10x } & = & 1 \color{blue}{+8} \\\Leftrightarrow &-7x & = &9\\\Leftrightarrow & \color{red}{-7}x & = &9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-8}& = & -2 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8-9x } & = & -2 \color{red}{ +9x }\color{blue}{+8-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -2 \color{blue}{+8} \\\Leftrightarrow &5x & = &6\\\Leftrightarrow & \color{red}{5}x & = &6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+11}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-x } & = & 11 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 11 \color{blue}{-11} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{-9}& = & 7 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{-9}\color{blue}{+9-14x } & = & 7 \color{red}{ +14x }\color{blue}{+9-14x } \\\Leftrightarrow & 11x \color{blue}{-14x } & = & 7 \color{blue}{+9} \\\Leftrightarrow &-3x & = &16\\\Leftrightarrow & \color{red}{-3}x & = &16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{-10}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-10}\color{blue}{+10-x } & = & -8 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -8 \color{blue}{+10} \\\Leftrightarrow &-10x & = &2\\\Leftrightarrow & \color{red}{-10}x & = &2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{-2}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-2}\color{blue}{+2-x } & = & 9 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 9 \color{blue}{+2} \\\Leftrightarrow &-15x & = &11\\\Leftrightarrow & \color{red}{-15}x & = &11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{15} } & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-3}& = & -15 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3-11x } & = & -15 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -15 \color{blue}{+3} \\\Leftrightarrow &-21x & = &-12\\\Leftrightarrow & \color{red}{-21}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-12}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{-3}& = & -8 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{-3}\color{blue}{+3-2x } & = & -8 \color{red}{ +2x }\color{blue}{+3-2x } \\\Leftrightarrow & -x \color{blue}{-2x } & = & -8 \color{blue}{+3} \\\Leftrightarrow &-3x & = &-5\\\Leftrightarrow & \color{red}{-3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+9}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+9}\color{blue}{-9-x } & = & -12 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -12 \color{blue}{-9} \\\Leftrightarrow &-7x & = &-21\\\Leftrightarrow & \color{red}{-7}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-21}{-7} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+11}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11-x } & = & 8 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 8 \color{blue}{-11} \\\Leftrightarrow &-16x & = &-3\\\Leftrightarrow & \color{red}{-16}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{16} } & & \\ & V = \left\{ \frac{3}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{-2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-2}\color{blue}{+2-x } & = & -10 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -10 \color{blue}{+2} \\\Leftrightarrow &-9x & = &-8\\\Leftrightarrow & \color{red}{-9}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-8}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{9} } & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+10}& = & 2 \color{red}{ +3x } \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10-3x } & = & 2 \color{red}{ +3x }\color{blue}{-10-3x } \\\Leftrightarrow & 5x \color{blue}{-3x } & = & 2 \color{blue}{-10} \\\Leftrightarrow &2x & = &-8\\\Leftrightarrow & \color{red}{2}x & = &-8\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-8}{2} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)