Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (3x+4)& = & -4 \color{red}{-} (-8+x) \\\Leftrightarrow & 12x+16& = &-4+8-x \\\Leftrightarrow & 12x \color{red}{+16} & = &4 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & 12x+x& = &4-16 \\\Leftrightarrow & 13x& = &-12 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-12}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-12}{13} & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (4x-6)& = & -11 \color{red}{+} (-10+x) \\\Leftrightarrow & 20x-30& = &-11-10+x \\\Leftrightarrow & 20x \color{red}{-30} & = &-21 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 20x-x& = &-21+30 \\\Leftrightarrow & 19x& = &9 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{9}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{9}{19} & & \\ & V = \left\{ \frac{9}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (5x+4)& = & -7 \color{red}{+} (9+x) \\\Leftrightarrow & 30x+24& = &-7+9+x \\\Leftrightarrow & 30x \color{red}{+24} & = &2 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 30x-x& = &2-24 \\\Leftrightarrow & 29x& = &-22 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-22}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-22}{29} & & \\ & V = \left\{ \frac{-22}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (5x+4)& = & 9 \color{red}{+} (-11-3x) \\\Leftrightarrow & 10x+8& = &9-11-3x \\\Leftrightarrow & 10x \color{red}{+8} & = &-2 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+8} \color{blue}{-8} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-8} \\\Leftrightarrow & 10x+3x& = &-2-8 \\\Leftrightarrow & 13x& = &-10 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-10}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (4x+7)& = & -2 \color{red}{+} (4+x) \\\Leftrightarrow & 16x+28& = &-2+4+x \\\Leftrightarrow & 16x \color{red}{+28} & = &2 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 16x-x& = &2-28 \\\Leftrightarrow & 15x& = &-26 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{-26}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{-26}{15} & & \\ & V = \left\{ \frac{-26}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (5x+3)& = & 15 \color{red}{-} (15+x) \\\Leftrightarrow & 25x+15& = &15-15-x \\\Leftrightarrow & 25x \color{red}{+15} & = &0 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 25x+x& = &0-15 \\\Leftrightarrow & 26x& = &-15 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{-15}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{-15}{26} & & \\ & V = \left\{ \frac{-15}{26} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-x-7)& = & 15 \color{red}{+} (10+3x) \\\Leftrightarrow & -4x-28& = &15+10+3x \\\Leftrightarrow & -4x \color{red}{-28} & = &25 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-28} \color{blue}{+28} \color{blue}{-3x} & = &25 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+28} \\\Leftrightarrow & -4x-3x& = &25+28 \\\Leftrightarrow & -7x& = &53 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{53}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-53}{7} & & \\ & V = \left\{ \frac{-53}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-4x+3)& = & -7 \color{red}{+} (-8+x) \\\Leftrightarrow & -8x+6& = &-7-8+x \\\Leftrightarrow & -8x \color{red}{+6} & = &-15 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -8x-x& = &-15-6 \\\Leftrightarrow & -9x& = &-21 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-21}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{7}{3} & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (3x-2)& = & 13 \color{red}{-} (-6-2x) \\\Leftrightarrow & 15x-10& = &13+6+2x \\\Leftrightarrow & 15x \color{red}{-10} & = &19 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-10} \color{blue}{+10} \color{blue}{-2x} & = &19 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+10} \\\Leftrightarrow & 15x-2x& = &19+10 \\\Leftrightarrow & 13x& = &29 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{29}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{29}{13} & & \\ & V = \left\{ \frac{29}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-2x-4)& = & -6 \color{red}{-} (14+x) \\\Leftrightarrow & -12x-24& = &-6-14-x \\\Leftrightarrow & -12x \color{red}{-24} & = &-20 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -12x+x& = &-20+24 \\\Leftrightarrow & -11x& = &4 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{4}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-4}{11} & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (5x+2)& = & -8 \color{red}{+} (10+x) \\\Leftrightarrow & 10x+4& = &-8+10+x \\\Leftrightarrow & 10x \color{red}{+4} & = &2 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 10x-x& = &2-4 \\\Leftrightarrow & 9x& = &-2 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-2}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-2}{9} & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-2x-1)& = & -15 \color{red}{-} (6+3x) \\\Leftrightarrow & -4x-2& = &-15-6-3x \\\Leftrightarrow & -4x \color{red}{-2} & = &-21 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-2} \color{blue}{+2} \color{blue}{+3x} & = &-21 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+2} \\\Leftrightarrow & -4x+3x& = &-21+2 \\\Leftrightarrow & -x& = &-19 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-19}{ \color{red}{-1} } \\\Leftrightarrow & x = 19 & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)