Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{3}{2})& = & -3x+\frac{2}{5} \\\Leftrightarrow & 35x+\frac{21}{2}& = & -3x+\frac{2}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{350}{ \color{blue}{10} }x+ \frac{105}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{4}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 350x \color{red}{+105} & = & \color{red}{-30x} +4 \\\Leftrightarrow & 350x \color{red}{+105} \color{blue}{-105} \color{blue}{+30x} & = & \color{red}{-30x} +4 \color{blue}{+30x} \color{blue}{-105} \\\Leftrightarrow & 350x+30x& = & 4-105 \\\Leftrightarrow & \color{red}{380} x& = & -101 \\\Leftrightarrow & x = \frac{-101}{380} & & \\ & V = \left\{ \frac{-101}{380} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{3}{10})& = & 5x+\frac{7}{8} \\\Leftrightarrow & -9x-\frac{9}{10}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 10 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-360}{ \color{blue}{40} }x- \frac{36}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -360x \color{red}{-36} & = & \color{red}{200x} +35 \\\Leftrightarrow & -360x \color{red}{-36} \color{blue}{+36} \color{blue}{-200x} & = & \color{red}{200x} +35 \color{blue}{-200x} \color{blue}{+36} \\\Leftrightarrow & -360x-200x& = & 35+36 \\\Leftrightarrow & \color{red}{-560} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-560} & & \\\Leftrightarrow & x = \frac{-71}{560} & & \\ & V = \left\{ \frac{-71}{560} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{4}{5})& = & -7x+\frac{4}{11} \\\Leftrightarrow & 15x-\frac{12}{5}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{-132} & = & \color{red}{-385x} +20 \\\Leftrightarrow & 825x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +20 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & 825x+385x& = & 20+132 \\\Leftrightarrow & \color{red}{1210} x& = & 152 \\\Leftrightarrow & x = \frac{152}{1210} & & \\\Leftrightarrow & x = \frac{76}{605} & & \\ & V = \left\{ \frac{76}{605} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{5}{4})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 12x+\frac{15}{4}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{336}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{16}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 336x \color{red}{+105} & = & \color{red}{140x} +16 \\\Leftrightarrow & 336x \color{red}{+105} \color{blue}{-105} \color{blue}{-140x} & = & \color{red}{140x} +16 \color{blue}{-140x} \color{blue}{-105} \\\Leftrightarrow & 336x-140x& = & 16-105 \\\Leftrightarrow & \color{red}{196} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{196} & & \\ & V = \left\{ \frac{-89}{196} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{3}{4})& = & 6x+\frac{5}{2} \\\Leftrightarrow & 25x-\frac{15}{4}& = & 6x+\frac{5}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{100}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{24}{ \color{blue}{4} }x+ \frac{10}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 100x \color{red}{-15} & = & \color{red}{24x} +10 \\\Leftrightarrow & 100x \color{red}{-15} \color{blue}{+15} \color{blue}{-24x} & = & \color{red}{24x} +10 \color{blue}{-24x} \color{blue}{+15} \\\Leftrightarrow & 100x-24x& = & 10+15 \\\Leftrightarrow & \color{red}{76} x& = & 25 \\\Leftrightarrow & x = \frac{25}{76} & & \\ & V = \left\{ \frac{25}{76} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{5}{11})& = & 5x+\frac{2}{11} \\\Leftrightarrow & 12x+\frac{15}{11}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x+ \frac{15}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{+15} & = & \color{red}{55x} +2 \\\Leftrightarrow & 132x \color{red}{+15} \color{blue}{-15} \color{blue}{-55x} & = & \color{red}{55x} +2 \color{blue}{-55x} \color{blue}{-15} \\\Leftrightarrow & 132x-55x& = & 2-15 \\\Leftrightarrow & \color{red}{77} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{77} & & \\ & V = \left\{ \frac{-13}{77} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{11})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 12x+\frac{12}{11}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{264}{ \color{blue}{22} }x+ \frac{24}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 264x \color{red}{+24} & = & \color{red}{110x} +99 \\\Leftrightarrow & 264x \color{red}{+24} \color{blue}{-24} \color{blue}{-110x} & = & \color{red}{110x} +99 \color{blue}{-110x} \color{blue}{-24} \\\Leftrightarrow & 264x-110x& = & 99-24 \\\Leftrightarrow & \color{red}{154} x& = & 75 \\\Leftrightarrow & x = \frac{75}{154} & & \\ & V = \left\{ \frac{75}{154} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{3}{4})& = & 7x+\frac{5}{6} \\\Leftrightarrow & 6x-\frac{9}{4}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 4 en 6 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{72}{ \color{blue}{12} }x- \frac{27}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{10}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 72x \color{red}{-27} & = & \color{red}{84x} +10 \\\Leftrightarrow & 72x \color{red}{-27} \color{blue}{+27} \color{blue}{-84x} & = & \color{red}{84x} +10 \color{blue}{-84x} \color{blue}{+27} \\\Leftrightarrow & 72x-84x& = & 10+27 \\\Leftrightarrow & \color{red}{-12} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-12} & & \\\Leftrightarrow & x = \frac{-37}{12} & & \\ & V = \left\{ \frac{-37}{12} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{4})& = & 4x+\frac{4}{3} \\\Leftrightarrow & -15x-\frac{15}{4}& = & 4x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{48}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{-45} & = & \color{red}{48x} +16 \\\Leftrightarrow & -180x \color{red}{-45} \color{blue}{+45} \color{blue}{-48x} & = & \color{red}{48x} +16 \color{blue}{-48x} \color{blue}{+45} \\\Leftrightarrow & -180x-48x& = & 16+45 \\\Leftrightarrow & \color{red}{-228} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-228} & & \\\Leftrightarrow & x = \frac{-61}{228} & & \\ & V = \left\{ \frac{-61}{228} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{3}{2})& = & -3x+\frac{3}{7} \\\Leftrightarrow & -14x+\frac{21}{2}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-196}{ \color{blue}{14} }x+ \frac{147}{ \color{blue}{14} })& = & (\frac{-42}{ \color{blue}{14} }x+ \frac{6}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -196x \color{red}{+147} & = & \color{red}{-42x} +6 \\\Leftrightarrow & -196x \color{red}{+147} \color{blue}{-147} \color{blue}{+42x} & = & \color{red}{-42x} +6 \color{blue}{+42x} \color{blue}{-147} \\\Leftrightarrow & -196x+42x& = & 6-147 \\\Leftrightarrow & \color{red}{-154} x& = & -141 \\\Leftrightarrow & x = \frac{-141}{-154} & & \\\Leftrightarrow & x = \frac{141}{154} & & \\ & V = \left\{ \frac{141}{154} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & -4x+\frac{10}{7} \\\Leftrightarrow & 21x-\frac{14}{3}& = & -4x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{441}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{-84}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 441x \color{red}{-98} & = & \color{red}{-84x} +30 \\\Leftrightarrow & 441x \color{red}{-98} \color{blue}{+98} \color{blue}{+84x} & = & \color{red}{-84x} +30 \color{blue}{+84x} \color{blue}{+98} \\\Leftrightarrow & 441x+84x& = & 30+98 \\\Leftrightarrow & \color{red}{525} x& = & 128 \\\Leftrightarrow & x = \frac{128}{525} & & \\ & V = \left\{ \frac{128}{525} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{2}{9})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -6x+\frac{4}{9}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{+4} & = & \color{red}{-63x} +6 \\\Leftrightarrow & -54x \color{red}{+4} \color{blue}{-4} \color{blue}{+63x} & = & \color{red}{-63x} +6 \color{blue}{+63x} \color{blue}{-4} \\\Leftrightarrow & -54x+63x& = & 6-4 \\\Leftrightarrow & \color{red}{9} x& = & 2 \\\Leftrightarrow & x = \frac{2}{9} & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)