Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-6x-7)& = & -11 \color{red}{+} (-14+x) \\\Leftrightarrow & -24x-28& = &-11-14+x \\\Leftrightarrow & -24x \color{red}{-28} & = &-25 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-25 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -24x-x& = &-25+28 \\\Leftrightarrow & -25x& = &3 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{3}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-3}{25} & & \\ & V = \left\{ \frac{-3}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-5x+5)& = & -14 \color{red}{+} (-4-3x) \\\Leftrightarrow & -25x+25& = &-14-4-3x \\\Leftrightarrow & -25x \color{red}{+25} & = &-18 \color{red}{-3x} \\\Leftrightarrow & -25x \color{red}{+25} \color{blue}{-25} \color{blue}{+3x} & = &-18 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-25} \\\Leftrightarrow & -25x+3x& = &-18-25 \\\Leftrightarrow & -22x& = &-43 \\\Leftrightarrow & \frac{-22x}{ \color{red}{-22} }& = &\frac{-43}{ \color{red}{-22} } \\\Leftrightarrow & x = \frac{43}{22} & & \\ & V = \left\{ \frac{43}{22} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (6x-7)& = & -6 \color{red}{+} (-11+x) \\\Leftrightarrow & 24x-28& = &-6-11+x \\\Leftrightarrow & 24x \color{red}{-28} & = &-17 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 24x-x& = &-17+28 \\\Leftrightarrow & 23x& = &11 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{11}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{11}{23} & & \\ & V = \left\{ \frac{11}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (6x-7)& = & 8 \color{red}{+} (-1+x) \\\Leftrightarrow & 36x-42& = &8-1+x \\\Leftrightarrow & 36x \color{red}{-42} & = &7 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 36x-x& = &7+42 \\\Leftrightarrow & 35x& = &49 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{49}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{7}{5} & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-3x+1)& = & 4 \color{red}{+} (8+x) \\\Leftrightarrow & -6x+2& = &4+8+x \\\Leftrightarrow & -6x \color{red}{+2} & = &12 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & -6x-x& = &12-2 \\\Leftrightarrow & -7x& = &10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-x-7)& = & -5 \color{red}{+} (4+x) \\\Leftrightarrow & -6x-42& = &-5+4+x \\\Leftrightarrow & -6x \color{red}{-42} & = &-1 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -6x-x& = &-1+42 \\\Leftrightarrow & -7x& = &41 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{41}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-41}{7} & & \\ & V = \left\{ \frac{-41}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-6x+4)& = & 15 \color{red}{+} (-1-5x) \\\Leftrightarrow & -36x+24& = &15-1-5x \\\Leftrightarrow & -36x \color{red}{+24} & = &14 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & -36x+5x& = &14-24 \\\Leftrightarrow & -31x& = &-10 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-10}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{10}{31} & & \\ & V = \left\{ \frac{10}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-2x+5)& = & 4 \color{red}{+} (-2+x) \\\Leftrightarrow & -12x+30& = &4-2+x \\\Leftrightarrow & -12x \color{red}{+30} & = &2 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -12x-x& = &2-30 \\\Leftrightarrow & -13x& = &-28 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-28}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{28}{13} & & \\ & V = \left\{ \frac{28}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (4x+1)& = & -9 \color{red}{-} (-8+x) \\\Leftrightarrow & 16x+4& = &-9+8-x \\\Leftrightarrow & 16x \color{red}{+4} & = &-1 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 16x+x& = &-1-4 \\\Leftrightarrow & 17x& = &-5 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-5}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-5}{17} & & \\ & V = \left\{ \frac{-5}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (6x-1)& = & 7 \color{red}{-} (-14+x) \\\Leftrightarrow & 24x-4& = &7+14-x \\\Leftrightarrow & 24x \color{red}{-4} & = &21 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 24x+x& = &21+4 \\\Leftrightarrow & 25x& = &25 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{25}{ \color{red}{25} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-6x+6)& = & -6 \color{red}{-} (-11+x) \\\Leftrightarrow & -36x+36& = &-6+11-x \\\Leftrightarrow & -36x \color{red}{+36} & = &5 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -36x+x& = &5-36 \\\Leftrightarrow & -35x& = &-31 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{-31}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{31}{35} & & \\ & V = \left\{ \frac{31}{35} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (5x+3)& = & -5 \color{red}{+} (3-2x) \\\Leftrightarrow & 15x+9& = &-5+3-2x \\\Leftrightarrow & 15x \color{red}{+9} & = &-2 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+9} \color{blue}{-9} \color{blue}{+2x} & = &-2 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-9} \\\Leftrightarrow & 15x+2x& = &-2-9 \\\Leftrightarrow & 17x& = &-11 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-11}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-11}{17} & & \\ & V = \left\{ \frac{-11}{17} \right\} & \\\end{align}\)