Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+7}& = & -11 \color{red}{ -3x } \\\Leftrightarrow & -x \color{red}{+7}\color{blue}{-7+3x } & = & -11 \color{red}{ -3x }\color{blue}{-7+3x } \\\Leftrightarrow & -x \color{blue}{+3x } & = & -11 \color{blue}{-7} \\\Leftrightarrow &2x & = &-18\\\Leftrightarrow & \color{red}{2}x & = &-18\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-18}{2} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-9}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9-x } & = & -1 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -1 \color{blue}{+9} \\\Leftrightarrow &7x & = &8\\\Leftrightarrow & \color{red}{7}x & = &8\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{8}{7} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+15}& = & 8 \color{red}{ +2x } \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15-2x } & = & 8 \color{red}{ +2x }\color{blue}{-15-2x } \\\Leftrightarrow & 15x \color{blue}{-2x } & = & 8 \color{blue}{-15} \\\Leftrightarrow &13x & = &-7\\\Leftrightarrow & \color{red}{13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+6}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6-11x } & = & -6 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & -6 \color{blue}{-6} \\\Leftrightarrow &-x & = &-12\\\Leftrightarrow & \color{red}{-}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-12}{-1} \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{-6}& = & -13 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{-6}\color{blue}{+6-8x } & = & -13 \color{red}{ +8x }\color{blue}{+6-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & -13 \color{blue}{+6} \\\Leftrightarrow &-3x & = &-7\\\Leftrightarrow & \color{red}{-3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+5}& = & 12 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5+15x } & = & 12 \color{red}{ -15x }\color{blue}{-5+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & 12 \color{blue}{-5} \\\Leftrightarrow &19x & = &7\\\Leftrightarrow & \color{red}{19}x & = &7\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{7}{19} \\\Leftrightarrow & \color{green}{ x = \frac{7}{19} } & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+1}& = & -11 \color{red}{ -x } \\\Leftrightarrow & x \color{red}{+1}\color{blue}{-1+x } & = & -11 \color{red}{ -x }\color{blue}{-1+x } \\\Leftrightarrow & x \color{blue}{+x } & = & -11 \color{blue}{-1} \\\Leftrightarrow &2x & = &-12\\\Leftrightarrow & \color{red}{2}x & = &-12\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-12}{2} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{+15}& = & 5 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15-4x } & = & 5 \color{red}{ +4x }\color{blue}{-15-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & 5 \color{blue}{-15} \\\Leftrightarrow &-7x & = &-10\\\Leftrightarrow & \color{red}{-7}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-11}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11-x } & = & 6 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 6 \color{blue}{+11} \\\Leftrightarrow &-7x & = &17\\\Leftrightarrow & \color{red}{-7}x & = &17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{7} } & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-7}& = & 12 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7+2x } & = & 12 \color{red}{ -2x }\color{blue}{+7+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & 12 \color{blue}{+7} \\\Leftrightarrow &13x & = &19\\\Leftrightarrow & \color{red}{13}x & = &19\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{19}{13} \\\Leftrightarrow & \color{green}{ x = \frac{19}{13} } & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+5}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5-x } & = & 2 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 2 \color{blue}{-5} \\\Leftrightarrow &-8x & = &-3\\\Leftrightarrow & \color{red}{-8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-11}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11-x } & = & 7 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &-5x & = &18\\\Leftrightarrow & \color{red}{-5}x & = &18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)