Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{+6}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-x } & = & -2 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -2 \color{blue}{-6} \\\Leftrightarrow &-6x & = &-8\\\Leftrightarrow & \color{red}{-6}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-8}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+15}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15-x } & = & -14 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -14 \color{blue}{-15} \\\Leftrightarrow &-12x & = &-29\\\Leftrightarrow & \color{red}{-12}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-29}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{29}{12} } & & \\ & V = \left\{ \frac{29}{12} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+10}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+10}\color{blue}{-10-x } & = & -2 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -2 \color{blue}{-10} \\\Leftrightarrow &-11x & = &-12\\\Leftrightarrow & \color{red}{-11}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-12}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+6}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+6}\color{blue}{-6-x } & = & 11 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 11 \color{blue}{-6} \\\Leftrightarrow &-7x & = &5\\\Leftrightarrow & \color{red}{-7}x & = &5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-1}& = & 7 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-1}\color{blue}{+1+7x } & = & 7 \color{red}{ -7x }\color{blue}{+1+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 7 \color{blue}{+1} \\\Leftrightarrow &15x & = &8\\\Leftrightarrow & \color{red}{15}x & = &8\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{8}{15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-3}& = & 6 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3-6x } & = & 6 \color{red}{ +6x }\color{blue}{+3-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & 6 \color{blue}{+3} \\\Leftrightarrow &-x & = &9\\\Leftrightarrow & \color{red}{-}x & = &9\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{9}{-1} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{-8}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8+11x } & = & -7 \color{red}{ -11x }\color{blue}{+8+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -7 \color{blue}{+8} \\\Leftrightarrow &15x & = &1\\\Leftrightarrow & \color{red}{15}x & = &1\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{1}{15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{+10}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+10}\color{blue}{-10-5x } & = & 2 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 2 \color{blue}{-10} \\\Leftrightarrow &x & = &-8\\\Leftrightarrow & \color{red}{}x & = &-8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -8 \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{+9}& = & 15 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9-11x } & = & 15 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 15 \color{blue}{-9} \\\Leftrightarrow &-18x & = &6\\\Leftrightarrow & \color{red}{-18}x & = &6\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{6}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+5}& = & 5 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-6x } & = & 5 \color{red}{ +6x }\color{blue}{-5-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 5 \color{blue}{-5} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{-7}& = & -7 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7+8x } & = & -7 \color{red}{ -8x }\color{blue}{+7+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{-13}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-13}\color{blue}{+13-x } & = & 13 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 13 \color{blue}{+13} \\\Leftrightarrow &-9x & = &26\\\Leftrightarrow & \color{red}{-9}x & = &26\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{26}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{9} } & & \\ & V = \left\{ \frac{-26}{9} \right\} & \\\end{align}\)