Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{+14}& = & -13 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14+9x } & = & -13 \color{red}{ -9x }\color{blue}{-14+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & -13 \color{blue}{-14} \\\Leftrightarrow &19x & = &-27\\\Leftrightarrow & \color{red}{19}x & = &-27\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-27}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{19} } & & \\ & V = \left\{ \frac{-27}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-4}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4-7x } & = & 4 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & 4 \color{blue}{+4} \\\Leftrightarrow &-4x & = &8\\\Leftrightarrow & \color{red}{-4}x & = &8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{8}{-4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+10}& = & 5 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+10}\color{blue}{-10+5x } & = & 5 \color{red}{ -5x }\color{blue}{-10+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 5 \color{blue}{-10} \\\Leftrightarrow &11x & = &-5\\\Leftrightarrow & \color{red}{11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-8}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-8}\color{blue}{+8-x } & = & -3 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -3 \color{blue}{+8} \\\Leftrightarrow &-13x & = &5\\\Leftrightarrow & \color{red}{-13}x & = &5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-8}& = & -3 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{-8}\color{blue}{+8-14x } & = & -3 \color{red}{ +14x }\color{blue}{+8-14x } \\\Leftrightarrow & 11x \color{blue}{-14x } & = & -3 \color{blue}{+8} \\\Leftrightarrow &-3x & = &5\\\Leftrightarrow & \color{red}{-3}x & = &5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+6}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+6}\color{blue}{-6-x } & = & -2 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -2 \color{blue}{-6} \\\Leftrightarrow &-15x & = &-8\\\Leftrightarrow & \color{red}{-15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-14}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-14}\color{blue}{+14-x } & = & 9 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 9 \color{blue}{+14} \\\Leftrightarrow &-6x & = &23\\\Leftrightarrow & \color{red}{-6}x & = &23\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{23}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{6} } & & \\ & V = \left\{ \frac{-23}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+2}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2-x } & = & 7 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 7 \color{blue}{-2} \\\Leftrightarrow &-12x & = &5\\\Leftrightarrow & \color{red}{-12}x & = &5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{+14}& = & 9 \color{red}{ -9x } \\\Leftrightarrow & 7x \color{red}{+14}\color{blue}{-14+9x } & = & 9 \color{red}{ -9x }\color{blue}{-14+9x } \\\Leftrightarrow & 7x \color{blue}{+9x } & = & 9 \color{blue}{-14} \\\Leftrightarrow &16x & = &-5\\\Leftrightarrow & \color{red}{16}x & = &-5\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-5}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{16} } & & \\ & V = \left\{ \frac{-5}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-1}& = & -10 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1-6x } & = & -10 \color{red}{ +6x }\color{blue}{+1-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -10 \color{blue}{+1} \\\Leftrightarrow &-11x & = &-9\\\Leftrightarrow & \color{red}{-11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{-10}& = & 5 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10-9x } & = & 5 \color{red}{ +9x }\color{blue}{+10-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & 5 \color{blue}{+10} \\\Leftrightarrow &-7x & = &15\\\Leftrightarrow & \color{red}{-7}x & = &15\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{15}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-11}& = & -7 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-11}\color{blue}{+11-9x } & = & -7 \color{red}{ +9x }\color{blue}{+11-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & -7 \color{blue}{+11} \\\Leftrightarrow &-x & = &4\\\Leftrightarrow & \color{red}{-}x & = &4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{4}{-1} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)