Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+1}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1-x } & = & -12 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -12 \color{blue}{-1} \\\Leftrightarrow &-13x & = &-13\\\Leftrightarrow & \color{red}{-13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-13}{-13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+6}& = & 7 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{+6}\color{blue}{-6-5x } & = & 7 \color{red}{ +5x }\color{blue}{-6-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &9x & = &1\\\Leftrightarrow & \color{red}{9}x & = &1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+7}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+7}\color{blue}{-7-13x } & = & -5 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -5 \color{blue}{-7} \\\Leftrightarrow &-25x & = &-12\\\Leftrightarrow & \color{red}{-25}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-12}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{12}{25} } & & \\ & V = \left\{ \frac{12}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+3}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-x } & = & -10 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -10 \color{blue}{-3} \\\Leftrightarrow &-4x & = &-13\\\Leftrightarrow & \color{red}{-4}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-13}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-6}& = & 9 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-6}\color{blue}{+6+11x } & = & 9 \color{red}{ -11x }\color{blue}{+6+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & 9 \color{blue}{+6} \\\Leftrightarrow &20x & = &15\\\Leftrightarrow & \color{red}{20}x & = &15\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{15}{20} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+4}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{+4}\color{blue}{-4-13x } & = & 4 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & 4 \color{blue}{-4} \\\Leftrightarrow &-10x & = &0\\\Leftrightarrow & \color{red}{-10}x & = &0\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{0}{-10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{-2}& = & -2 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2+3x } & = & -2 \color{red}{ -3x }\color{blue}{+2+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -2 \color{blue}{+2} \\\Leftrightarrow &7x & = &0\\\Leftrightarrow & \color{red}{7}x & = &0\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{0}{7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-2}& = & 14 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2+10x } & = & 14 \color{red}{ -10x }\color{blue}{+2+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & 14 \color{blue}{+2} \\\Leftrightarrow &17x & = &16\\\Leftrightarrow & \color{red}{17}x & = &16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{16}{17} } & & \\ & V = \left\{ \frac{16}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-10}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-10}\color{blue}{+10-x } & = & -1 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -1 \color{blue}{+10} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-2}& = & -8 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-2}\color{blue}{+2+9x } & = & -8 \color{red}{ -9x }\color{blue}{+2+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -8 \color{blue}{+2} \\\Leftrightarrow &14x & = &-6\\\Leftrightarrow & \color{red}{14}x & = &-6\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-6}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{-4}& = & 3 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-4}\color{blue}{+4+13x } & = & 3 \color{red}{ -13x }\color{blue}{+4+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 3 \color{blue}{+4} \\\Leftrightarrow &22x & = &7\\\Leftrightarrow & \color{red}{22}x & = &7\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{7}{22} \\\Leftrightarrow & \color{green}{ x = \frac{7}{22} } & & \\ & V = \left\{ \frac{7}{22} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+1}& = & 13 \color{red}{ +12x } \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1-12x } & = & 13 \color{red}{ +12x }\color{blue}{-1-12x } \\\Leftrightarrow & 5x \color{blue}{-12x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &-7x & = &12\\\Leftrightarrow & \color{red}{-7}x & = &12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)