Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+9}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+9}\color{blue}{-9-7x } & = & 3 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & 3 \color{blue}{-9} \\\Leftrightarrow &-4x & = &-6\\\Leftrightarrow & \color{red}{-4}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-6}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{+14}& = & -4 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+14}\color{blue}{-14-4x } & = & -4 \color{red}{ +4x }\color{blue}{-14-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &-7x & = &-18\\\Leftrightarrow & \color{red}{-7}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{18}{7} } & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+7}& = & -14 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7+7x } & = & -14 \color{red}{ -7x }\color{blue}{-7+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -14 \color{blue}{-7} \\\Leftrightarrow &22x & = &-21\\\Leftrightarrow & \color{red}{22}x & = &-21\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-21}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{22} } & & \\ & V = \left\{ \frac{-21}{22} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+15}& = & 8 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15-7x } & = & 8 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & 8 \color{blue}{-15} \\\Leftrightarrow &x & = &-7\\\Leftrightarrow & \color{red}{}x & = &-7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -7 \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{-10}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-10}\color{blue}{+10+2x } & = & 2 \color{red}{ -2x }\color{blue}{+10+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 2 \color{blue}{+10} \\\Leftrightarrow &17x & = &12\\\Leftrightarrow & \color{red}{17}x & = &12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{12}{17} } & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+8}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+8}\color{blue}{-8-x } & = & 15 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 15 \color{blue}{-8} \\\Leftrightarrow &-14x & = &7\\\Leftrightarrow & \color{red}{-14}x & = &7\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{7}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+7}& = & 5 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7-7x } & = & 5 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & 5 \color{blue}{-7} \\\Leftrightarrow &5x & = &-2\\\Leftrightarrow & \color{red}{5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+7}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-x } & = & -3 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -3 \color{blue}{-7} \\\Leftrightarrow &x & = &-10\\\Leftrightarrow & \color{red}{}x & = &-10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -10 \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-5}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & 7x \color{red}{-5}\color{blue}{+5-9x } & = & 3 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & 7x \color{blue}{-9x } & = & 3 \color{blue}{+5} \\\Leftrightarrow &-2x & = &8\\\Leftrightarrow & \color{red}{-2}x & = &8\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{8}{-2} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{+15}& = & -13 \color{red}{ -x } \\\Leftrightarrow & x \color{red}{+15}\color{blue}{-15+x } & = & -13 \color{red}{ -x }\color{blue}{-15+x } \\\Leftrightarrow & x \color{blue}{+x } & = & -13 \color{blue}{-15} \\\Leftrightarrow &2x & = &-28\\\Leftrightarrow & \color{red}{2}x & = &-28\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-28}{2} \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+6}& = & 5 \color{red}{ +9x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6-9x } & = & 5 \color{red}{ +9x }\color{blue}{-6-9x } \\\Leftrightarrow & 5x \color{blue}{-9x } & = & 5 \color{blue}{-6} \\\Leftrightarrow &-4x & = &-1\\\Leftrightarrow & \color{red}{-4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+4}& = & -14 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+4}\color{blue}{-4-3x } & = & -14 \color{red}{ +3x }\color{blue}{-4-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &-8x & = &-18\\\Leftrightarrow & \color{red}{-8}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-18}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)