Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-14}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14-5x } & = & 11 \color{red}{ +5x }\color{blue}{+14-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 11 \color{blue}{+14} \\\Leftrightarrow &x & = &25\\\Leftrightarrow & \color{red}{}x & = &25\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 25 \\\Leftrightarrow & \color{green}{ x = 25 } & & \\ & V = \left\{ 25 \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+12}& = & -8 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12+5x } & = & -8 \color{red}{ -5x }\color{blue}{-12+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &11x & = &-20\\\Leftrightarrow & \color{red}{11}x & = &-20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{11} } & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-2}& = & -1 \color{red}{ -2x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2+2x } & = & -1 \color{red}{ -2x }\color{blue}{+2+2x } \\\Leftrightarrow & 7x \color{blue}{+2x } & = & -1 \color{blue}{+2} \\\Leftrightarrow &9x & = &1\\\Leftrightarrow & \color{red}{9}x & = &1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-14}& = & -12 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{-14}\color{blue}{+14-9x } & = & -12 \color{red}{ +9x }\color{blue}{+14-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & -12 \color{blue}{+14} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{+8}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8-x } & = & 5 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 5 \color{blue}{-8} \\\Leftrightarrow &-15x & = &-3\\\Leftrightarrow & \color{red}{-15}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{-11}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-x } & = & 6 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 6 \color{blue}{+11} \\\Leftrightarrow &-15x & = &17\\\Leftrightarrow & \color{red}{-15}x & = &17\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{17}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{15} } & & \\ & V = \left\{ \frac{-17}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-15}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{-15}\color{blue}{+15-5x } & = & 2 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & 2 \color{blue}{+15} \\\Leftrightarrow &-7x & = &17\\\Leftrightarrow & \color{red}{-7}x & = &17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{7} } & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{+3}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3-x } & = & -12 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -12 \color{blue}{-3} \\\Leftrightarrow &-13x & = &-15\\\Leftrightarrow & \color{red}{-13}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-15}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{15}{13} } & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-15}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-x } & = & -9 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -9 \color{blue}{+15} \\\Leftrightarrow &-7x & = &6\\\Leftrightarrow & \color{red}{-7}x & = &6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-10}& = & -15 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10+14x } & = & -15 \color{red}{ -14x }\color{blue}{+10+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -15 \color{blue}{+10} \\\Leftrightarrow &19x & = &-5\\\Leftrightarrow & \color{red}{19}x & = &-5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{19} } & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+4}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4-x } & = & 4 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 4 \color{blue}{-4} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{-1}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-1}\color{blue}{+1-x } & = & 3 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 3 \color{blue}{+1} \\\Leftrightarrow &-7x & = &4\\\Leftrightarrow & \color{red}{-7}x & = &4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)