Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{-2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2-x } & = & -3 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -3 \color{blue}{+2} \\\Leftrightarrow &8x & = &-1\\\Leftrightarrow & \color{red}{8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+11}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11-x } & = & -4 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -4 \color{blue}{-11} \\\Leftrightarrow &-6x & = &-15\\\Leftrightarrow & \color{red}{-6}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-15}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-9}& = & 6 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-6x } & = & 6 \color{red}{ +6x }\color{blue}{+9-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &-11x & = &15\\\Leftrightarrow & \color{red}{-11}x & = &15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{11} } & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+8}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8-x } & = & -7 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -7 \color{blue}{-8} \\\Leftrightarrow &-3x & = &-15\\\Leftrightarrow & \color{red}{-3}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-15}{-3} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+10}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+10}\color{blue}{-10-7x } & = & 9 \color{red}{ +7x }\color{blue}{-10-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & 9 \color{blue}{-10} \\\Leftrightarrow &-4x & = &-1\\\Leftrightarrow & \color{red}{-4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-1}& = & 8 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1-9x } & = & 8 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 8 \color{blue}{+1} \\\Leftrightarrow &-17x & = &9\\\Leftrightarrow & \color{red}{-17}x & = &9\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{9}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{17} } & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-2}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-2}\color{blue}{+2-x } & = & -11 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -11 \color{blue}{+2} \\\Leftrightarrow &-12x & = &-9\\\Leftrightarrow & \color{red}{-12}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-9}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{-9}& = & 9 \color{red}{ -2x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9+2x } & = & 9 \color{red}{ -2x }\color{blue}{+9+2x } \\\Leftrightarrow & x \color{blue}{+2x } & = & 9 \color{blue}{+9} \\\Leftrightarrow &3x & = &18\\\Leftrightarrow & \color{red}{3}x & = &18\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{18}{3} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{+15}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+15}\color{blue}{-15-11x } & = & -9 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -9 \color{blue}{-15} \\\Leftrightarrow &-16x & = &-24\\\Leftrightarrow & \color{red}{-16}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-24}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-4}& = & 13 \color{red}{ -4x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4+4x } & = & 13 \color{red}{ -4x }\color{blue}{+4+4x } \\\Leftrightarrow & 13x \color{blue}{+4x } & = & 13 \color{blue}{+4} \\\Leftrightarrow &17x & = &17\\\Leftrightarrow & \color{red}{17}x & = &17\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{17}{17} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{-9}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-7x } & = & 15 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 15 \color{blue}{+9} \\\Leftrightarrow &-20x & = &24\\\Leftrightarrow & \color{red}{-20}x & = &24\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{24}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-10}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-10}\color{blue}{+10-x } & = & 8 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 8 \color{blue}{+10} \\\Leftrightarrow &7x & = &18\\\Leftrightarrow & \color{red}{7}x & = &18\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{18}{7} \\\Leftrightarrow & \color{green}{ x = \frac{18}{7} } & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)