Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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