Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (4x+7)& = & -13 \color{red}{+} (6+x) \\\Leftrightarrow & 8x+14& = &-13+6+x \\\Leftrightarrow & 8x \color{red}{+14} & = &-7 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & 8x-x& = &-7-14 \\\Leftrightarrow & 7x& = &-21 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-21}{ \color{red}{7} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (x-7)& = & 4 \color{red}{-} (-4+2x) \\\Leftrightarrow & 5x-35& = &4+4-2x \\\Leftrightarrow & 5x \color{red}{-35} & = &8 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{-35} \color{blue}{+35} \color{blue}{+2x} & = &8 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+35} \\\Leftrightarrow & 5x+2x& = &8+35 \\\Leftrightarrow & 7x& = &43 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{43}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{43}{7} & & \\ & V = \left\{ \frac{43}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-6x-5)& = & -5 \color{red}{+} (-15-5x) \\\Leftrightarrow & -18x-15& = &-5-15-5x \\\Leftrightarrow & -18x \color{red}{-15} & = &-20 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-15} \color{blue}{+15} \color{blue}{+5x} & = &-20 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+15} \\\Leftrightarrow & -18x+5x& = &-20+15 \\\Leftrightarrow & -13x& = &-5 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-5}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{5}{13} & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (5x+6)& = & -10 \color{red}{-} (8+x) \\\Leftrightarrow & 25x+30& = &-10-8-x \\\Leftrightarrow & 25x \color{red}{+30} & = &-18 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 25x+x& = &-18-30 \\\Leftrightarrow & 26x& = &-48 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{-48}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{-24}{13} & & \\ & V = \left\{ \frac{-24}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (x-3)& = & 10 \color{red}{+} (1+x) \\\Leftrightarrow & 3x-9& = &10+1+x \\\Leftrightarrow & 3x \color{red}{-9} & = &11 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & 3x-x& = &11+9 \\\Leftrightarrow & 2x& = &20 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{20}{ \color{red}{2} } \\\Leftrightarrow & x = 10 & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (2x+4)& = & 1 \color{red}{-} (-4+x) \\\Leftrightarrow & 4x+8& = &1+4-x \\\Leftrightarrow & 4x \color{red}{+8} & = &5 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 4x+x& = &5-8 \\\Leftrightarrow & 5x& = &-3 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-3}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-3}{5} & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-4x-7)& = & -14 \color{red}{-} (11+x) \\\Leftrightarrow & -8x-14& = &-14-11-x \\\Leftrightarrow & -8x \color{red}{-14} & = &-25 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &-25 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & -8x+x& = &-25+14 \\\Leftrightarrow & -7x& = &-11 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-11}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{11}{7} & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (5x+6)& = & 10 \color{red}{+} (10+x) \\\Leftrightarrow & 30x+36& = &10+10+x \\\Leftrightarrow & 30x \color{red}{+36} & = &20 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & 30x-x& = &20-36 \\\Leftrightarrow & 29x& = &-16 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-16}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-16}{29} & & \\ & V = \left\{ \frac{-16}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-4x+7)& = & -6 \color{red}{-} (10-5x) \\\Leftrightarrow & -16x+28& = &-6-10+5x \\\Leftrightarrow & -16x \color{red}{+28} & = &-16 \color{red}{+5x} \\\Leftrightarrow & -16x \color{red}{+28} \color{blue}{-28} \color{blue}{-5x} & = &-16 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-28} \\\Leftrightarrow & -16x-5x& = &-16-28 \\\Leftrightarrow & -21x& = &-44 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-44}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{44}{21} & & \\ & V = \left\{ \frac{44}{21} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (5x+7)& = & 11 \color{red}{+} (1+4x) \\\Leftrightarrow & 15x+21& = &11+1+4x \\\Leftrightarrow & 15x \color{red}{+21} & = &12 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{+21} \color{blue}{-21} \color{blue}{-4x} & = &12 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-21} \\\Leftrightarrow & 15x-4x& = &12-21 \\\Leftrightarrow & 11x& = &-9 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-9}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-9}{11} & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-2x-3)& = & -10 \color{red}{+} (-3+x) \\\Leftrightarrow & -12x-18& = &-10-3+x \\\Leftrightarrow & -12x \color{red}{-18} & = &-13 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -12x-x& = &-13+18 \\\Leftrightarrow & -13x& = &5 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{5}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-x-3)& = & 4 \color{red}{-} (2+x) \\\Leftrightarrow & -6x-18& = &4-2-x \\\Leftrightarrow & -6x \color{red}{-18} & = &2 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -6x+x& = &2+18 \\\Leftrightarrow & -5x& = &20 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{20}{ \color{red}{-5} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)