Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-1}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-1}\color{blue}{+1-x } & = & 15 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &-7x & = &16\\\Leftrightarrow & \color{red}{-7}x & = &16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{7} } & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{+14}& = & 9 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14+6x } & = & 9 \color{red}{ -6x }\color{blue}{-14+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 9 \color{blue}{-14} \\\Leftrightarrow &19x & = &-5\\\Leftrightarrow & \color{red}{19}x & = &-5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{19} } & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{-11}& = & -12 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{-11}\color{blue}{+11-10x } & = & -12 \color{red}{ +10x }\color{blue}{+11-10x } \\\Leftrightarrow & 13x \color{blue}{-10x } & = & -12 \color{blue}{+11} \\\Leftrightarrow &3x & = &-1\\\Leftrightarrow & \color{red}{3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+15}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+15}\color{blue}{-15-x } & = & -10 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -10 \color{blue}{-15} \\\Leftrightarrow &11x & = &-25\\\Leftrightarrow & \color{red}{11}x & = &-25\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-25}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{11} } & & \\ & V = \left\{ \frac{-25}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-8}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-x } & = & 3 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 3 \color{blue}{+8} \\\Leftrightarrow &-14x & = &11\\\Leftrightarrow & \color{red}{-14}x & = &11\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{11}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{14} } & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+5}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-5x } & = & 10 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & 10 \color{blue}{-5} \\\Leftrightarrow &-19x & = &5\\\Leftrightarrow & \color{red}{-19}x & = &5\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{5}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{19} } & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-11}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-11}\color{blue}{+11-9x } & = & -5 \color{red}{ +9x }\color{blue}{+11-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -5 \color{blue}{+11} \\\Leftrightarrow &-17x & = &6\\\Leftrightarrow & \color{red}{-17}x & = &6\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{6}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{17} } & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{-4}& = & -7 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4-4x } & = & -7 \color{red}{ +4x }\color{blue}{+4-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & -7 \color{blue}{+4} \\\Leftrightarrow &11x & = &-3\\\Leftrightarrow & \color{red}{11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-10}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{-10}\color{blue}{+10-7x } & = & 9 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & 9 \color{blue}{+10} \\\Leftrightarrow &x & = &19\\\Leftrightarrow & \color{red}{}x & = &19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 19 \\\Leftrightarrow & \color{green}{ x = 19 } & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-11}& = & -15 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-11}\color{blue}{+11+7x } & = & -15 \color{red}{ -7x }\color{blue}{+11+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -15 \color{blue}{+11} \\\Leftrightarrow &15x & = &-4\\\Leftrightarrow & \color{red}{15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-4}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+9}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+9}\color{blue}{-9-x } & = & -5 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & -5 \color{blue}{-9} \\\Leftrightarrow &12x & = &-14\\\Leftrightarrow & \color{red}{12}x & = &-14\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-14}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+1}& = & 1 \color{red}{ +3x } \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1-3x } & = & 1 \color{red}{ +3x }\color{blue}{-1-3x } \\\Leftrightarrow & 5x \color{blue}{-3x } & = & 1 \color{blue}{-1} \\\Leftrightarrow &2x & = &0\\\Leftrightarrow & \color{red}{2}x & = &0\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{0}{2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)