Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(-10x+1=-10+x\)
2. \(15x-2=-8-7x\)
3. \(3x-2=2+8x\)
4. \(-5x+3=-6+x\)
5. \(-4x+6=15+x\)
6. \(15x+6=3-14x\)
7. \(4x-10=-2+11x\)
8. \(-2x+4=4+x\)
9. \(-13x-4=10+11x\)
10. \(-11x+3=8+4x\)
11. \(-x-2=7-9x\)
12. \(6x+7=2+x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+1}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+1}\color{blue}{-1-x } & = & -10 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -10 \color{blue}{-1} \\\Leftrightarrow &-11x & = &-11\\\Leftrightarrow & \color{red}{-11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-11}{-11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-2}& = & -8 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-2}\color{blue}{+2+7x } & = & -8 \color{red}{ -7x }\color{blue}{+2+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -8 \color{blue}{+2} \\\Leftrightarrow &22x & = &-6\\\Leftrightarrow & \color{red}{22}x & = &-6\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-6}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-2}& = & 2 \color{red}{ +8x } \\\Leftrightarrow & 3x \color{red}{-2}\color{blue}{+2-8x } & = & 2 \color{red}{ +8x }\color{blue}{+2-8x } \\\Leftrightarrow & 3x \color{blue}{-8x } & = & 2 \color{blue}{+2} \\\Leftrightarrow &-5x & = &4\\\Leftrightarrow & \color{red}{-5}x & = &4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{+3}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3-x } & = & -6 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -6 \color{blue}{-3} \\\Leftrightarrow &-6x & = &-9\\\Leftrightarrow & \color{red}{-6}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+6}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6-x } & = & 15 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 15 \color{blue}{-6} \\\Leftrightarrow &-5x & = &9\\\Leftrightarrow & \color{red}{-5}x & = &9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+6}& = & 3 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6+14x } & = & 3 \color{red}{ -14x }\color{blue}{-6+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 3 \color{blue}{-6} \\\Leftrightarrow &29x & = &-3\\\Leftrightarrow & \color{red}{29}x & = &-3\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-3}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{29} } & & \\ & V = \left\{ \frac{-3}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{-10}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{-10}\color{blue}{+10-11x } & = & -2 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & -2 \color{blue}{+10} \\\Leftrightarrow &-7x & = &8\\\Leftrightarrow & \color{red}{-7}x & = &8\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{8}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+4}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4-x } & = & 4 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 4 \color{blue}{-4} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-4}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & -13x \color{red}{-4}\color{blue}{+4-11x } & = & 10 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & -13x \color{blue}{-11x } & = & 10 \color{blue}{+4} \\\Leftrightarrow &-24x & = &14\\\Leftrightarrow & \color{red}{-24}x & = &14\\\Leftrightarrow & \frac{\color{red}{-24}x}{ \color{blue}{ -24}} & = & \frac{14}{-24} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{12} } & & \\ & V = \left\{ \frac{-7}{12} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{+3}& = & 8 \color{red}{ +4x } \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3-4x } & = & 8 \color{red}{ +4x }\color{blue}{-3-4x } \\\Leftrightarrow & -11x \color{blue}{-4x } & = & 8 \color{blue}{-3} \\\Leftrightarrow &-15x & = &5\\\Leftrightarrow & \color{red}{-15}x & = &5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{-2}& = & 7 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{-2}\color{blue}{+2+9x } & = & 7 \color{red}{ -9x }\color{blue}{+2+9x } \\\Leftrightarrow & -x \color{blue}{+9x } & = & 7 \color{blue}{+2} \\\Leftrightarrow &8x & = &9\\\Leftrightarrow & \color{red}{8}x & = &9\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{9}{8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+7}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7-x } & = & 2 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 2 \color{blue}{-7} \\\Leftrightarrow &5x & = &-5\\\Leftrightarrow & \color{red}{5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-5}{5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)