Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+10}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+10}\color{blue}{-10-5x } & = & -11 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -11 \color{blue}{-10} \\\Leftrightarrow &-9x & = &-21\\\Leftrightarrow & \color{red}{-9}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-21}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-2}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2-x } & = & 10 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 10 \color{blue}{+2} \\\Leftrightarrow &-16x & = &12\\\Leftrightarrow & \color{red}{-16}x & = &12\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{12}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+5}& = & -7 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5-3x } & = & -7 \color{red}{ +3x }\color{blue}{-5-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & -7 \color{blue}{-5} \\\Leftrightarrow &x & = &-12\\\Leftrightarrow & \color{red}{}x & = &-12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -12 \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-15}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-x } & = & -8 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -8 \color{blue}{+15} \\\Leftrightarrow &-7x & = &7\\\Leftrightarrow & \color{red}{-7}x & = &7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{7}{-7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+6}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6-x } & = & 14 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 14 \color{blue}{-6} \\\Leftrightarrow &-9x & = &8\\\Leftrightarrow & \color{red}{-9}x & = &8\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{8}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-2}& = & -9 \color{red}{ +10x } \\\Leftrightarrow & -x \color{red}{-2}\color{blue}{+2-10x } & = & -9 \color{red}{ +10x }\color{blue}{+2-10x } \\\Leftrightarrow & -x \color{blue}{-10x } & = & -9 \color{blue}{+2} \\\Leftrightarrow &-11x & = &-7\\\Leftrightarrow & \color{red}{-11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-3}& = & 14 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-3}\color{blue}{+3+8x } & = & 14 \color{red}{ -8x }\color{blue}{+3+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & 14 \color{blue}{+3} \\\Leftrightarrow &17x & = &17\\\Leftrightarrow & \color{red}{17}x & = &17\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{17}{17} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+11}& = & 15 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+11}\color{blue}{-11+3x } & = & 15 \color{red}{ -3x }\color{blue}{-11+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 15 \color{blue}{-11} \\\Leftrightarrow &13x & = &4\\\Leftrightarrow & \color{red}{13}x & = &4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-5}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-x } & = & 8 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 8 \color{blue}{+5} \\\Leftrightarrow &-9x & = &13\\\Leftrightarrow & \color{red}{-9}x & = &13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+8}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8-5x } & = & -8 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & -8 \color{blue}{-8} \\\Leftrightarrow &3x & = &-16\\\Leftrightarrow & \color{red}{3}x & = &-16\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-16}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-15}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15-5x } & = & 14 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 14 \color{blue}{+15} \\\Leftrightarrow &-9x & = &29\\\Leftrightarrow & \color{red}{-9}x & = &29\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{29}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{9} } & & \\ & V = \left\{ \frac{-29}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-4}& = & 5 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{-4}\color{blue}{+4+8x } & = & 5 \color{red}{ -8x }\color{blue}{+4+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & 5 \color{blue}{+4} \\\Leftrightarrow &19x & = &9\\\Leftrightarrow & \color{red}{19}x & = &9\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{9}{19} \\\Leftrightarrow & \color{green}{ x = \frac{9}{19} } & & \\ & V = \left\{ \frac{9}{19} \right\} & \\\end{align}\)