Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{4}{7})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -25x+\frac{20}{7}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-175}{ \color{blue}{7} }x+ \frac{20}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -175x \color{red}{+20} & = & \color{red}{-35x} +2 \\\Leftrightarrow & -175x \color{red}{+20} \color{blue}{-20} \color{blue}{+35x} & = & \color{red}{-35x} +2 \color{blue}{+35x} \color{blue}{-20} \\\Leftrightarrow & -175x+35x& = & 2-20 \\\Leftrightarrow & \color{red}{-140} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-140} & & \\\Leftrightarrow & x = \frac{9}{70} & & \\ & V = \left\{ \frac{9}{70} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{2}{7})& = & -5x+\frac{3}{7} \\\Leftrightarrow & -12x-\frac{6}{7}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{-6} & = & \color{red}{-35x} +3 \\\Leftrightarrow & -84x \color{red}{-6} \color{blue}{+6} \color{blue}{+35x} & = & \color{red}{-35x} +3 \color{blue}{+35x} \color{blue}{+6} \\\Leftrightarrow & -84x+35x& = & 3+6 \\\Leftrightarrow & \color{red}{-49} x& = & 9 \\\Leftrightarrow & x = \frac{9}{-49} & & \\\Leftrightarrow & x = \frac{-9}{49} & & \\ & V = \left\{ \frac{-9}{49} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{8})& = & 2x+\frac{6}{5} \\\Leftrightarrow & 21x+\frac{21}{8}& = & 2x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{840}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{80}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 840x \color{red}{+105} & = & \color{red}{80x} +48 \\\Leftrightarrow & 840x \color{red}{+105} \color{blue}{-105} \color{blue}{-80x} & = & \color{red}{80x} +48 \color{blue}{-80x} \color{blue}{-105} \\\Leftrightarrow & 840x-80x& = & 48-105 \\\Leftrightarrow & \color{red}{760} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{760} & & \\\Leftrightarrow & x = \frac{-3}{40} & & \\ & V = \left\{ \frac{-3}{40} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{2}{5})& = & 3x+\frac{9}{7} \\\Leftrightarrow & -14x+\frac{14}{5}& = & 3x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-490}{ \color{blue}{35} }x+ \frac{98}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -490x \color{red}{+98} & = & \color{red}{105x} +45 \\\Leftrightarrow & -490x \color{red}{+98} \color{blue}{-98} \color{blue}{-105x} & = & \color{red}{105x} +45 \color{blue}{-105x} \color{blue}{-98} \\\Leftrightarrow & -490x-105x& = & 45-98 \\\Leftrightarrow & \color{red}{-595} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{-595} & & \\\Leftrightarrow & x = \frac{53}{595} & & \\ & V = \left\{ \frac{53}{595} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{11})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -10x-\frac{10}{11}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-220}{ \color{blue}{22} }x- \frac{20}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -220x \color{red}{-20} & = & \color{red}{154x} +33 \\\Leftrightarrow & -220x \color{red}{-20} \color{blue}{+20} \color{blue}{-154x} & = & \color{red}{154x} +33 \color{blue}{-154x} \color{blue}{+20} \\\Leftrightarrow & -220x-154x& = & 33+20 \\\Leftrightarrow & \color{red}{-374} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-374} & & \\\Leftrightarrow & x = \frac{-53}{374} & & \\ & V = \left\{ \frac{-53}{374} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{4}{5})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 6x-\frac{12}{5}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{90}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 90x \color{red}{-36} & = & \color{red}{-75x} +10 \\\Leftrightarrow & 90x \color{red}{-36} \color{blue}{+36} \color{blue}{+75x} & = & \color{red}{-75x} +10 \color{blue}{+75x} \color{blue}{+36} \\\Leftrightarrow & 90x+75x& = & 10+36 \\\Leftrightarrow & \color{red}{165} x& = & 46 \\\Leftrightarrow & x = \frac{46}{165} & & \\ & V = \left\{ \frac{46}{165} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{3}{8})& = & -3x+\frac{8}{7} \\\Leftrightarrow & 28x+\frac{21}{8}& = & -3x+\frac{8}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1568}{ \color{blue}{56} }x+ \frac{147}{ \color{blue}{56} })& = & (\frac{-168}{ \color{blue}{56} }x+ \frac{64}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1568x \color{red}{+147} & = & \color{red}{-168x} +64 \\\Leftrightarrow & 1568x \color{red}{+147} \color{blue}{-147} \color{blue}{+168x} & = & \color{red}{-168x} +64 \color{blue}{+168x} \color{blue}{-147} \\\Leftrightarrow & 1568x+168x& = & 64-147 \\\Leftrightarrow & \color{red}{1736} x& = & -83 \\\Leftrightarrow & x = \frac{-83}{1736} & & \\ & V = \left\{ \frac{-83}{1736} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{5}{7})& = & 7x+\frac{9}{4} \\\Leftrightarrow & -10x-\frac{10}{7}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-280}{ \color{blue}{28} }x- \frac{40}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -280x \color{red}{-40} & = & \color{red}{196x} +63 \\\Leftrightarrow & -280x \color{red}{-40} \color{blue}{+40} \color{blue}{-196x} & = & \color{red}{196x} +63 \color{blue}{-196x} \color{blue}{+40} \\\Leftrightarrow & -280x-196x& = & 63+40 \\\Leftrightarrow & \color{red}{-476} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-476} & & \\\Leftrightarrow & x = \frac{-103}{476} & & \\ & V = \left\{ \frac{-103}{476} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{2}{3})& = & -6x+\frac{10}{11} \\\Leftrightarrow & 35x+\frac{14}{3}& = & -6x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{-198}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{+154} & = & \color{red}{-198x} +30 \\\Leftrightarrow & 1155x \color{red}{+154} \color{blue}{-154} \color{blue}{+198x} & = & \color{red}{-198x} +30 \color{blue}{+198x} \color{blue}{-154} \\\Leftrightarrow & 1155x+198x& = & 30-154 \\\Leftrightarrow & \color{red}{1353} x& = & -124 \\\Leftrightarrow & x = \frac{-124}{1353} & & \\ & V = \left\{ \frac{-124}{1353} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{5}{7})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{70}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 70x \color{red}{-10} & = & \color{red}{49x} +10 \\\Leftrightarrow & 70x \color{red}{-10} \color{blue}{+10} \color{blue}{-49x} & = & \color{red}{49x} +10 \color{blue}{-49x} \color{blue}{+10} \\\Leftrightarrow & 70x-49x& = & 10+10 \\\Leftrightarrow & \color{red}{21} x& = & 20 \\\Leftrightarrow & x = \frac{20}{21} & & \\ & V = \left\{ \frac{20}{21} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{2}{3})& = & -3x+\frac{10}{9} \\\Leftrightarrow & 8x-\frac{8}{3}& = & -3x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x- \frac{24}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{-24} & = & \color{red}{-27x} +10 \\\Leftrightarrow & 72x \color{red}{-24} \color{blue}{+24} \color{blue}{+27x} & = & \color{red}{-27x} +10 \color{blue}{+27x} \color{blue}{+24} \\\Leftrightarrow & 72x+27x& = & 10+24 \\\Leftrightarrow & \color{red}{99} x& = & 34 \\\Leftrightarrow & x = \frac{34}{99} & & \\ & V = \left\{ \frac{34}{99} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{4}{7})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -30x+\frac{24}{7}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x+ \frac{264}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{+264} & = & \color{red}{539x} +70 \\\Leftrightarrow & -2310x \color{red}{+264} \color{blue}{-264} \color{blue}{-539x} & = & \color{red}{539x} +70 \color{blue}{-539x} \color{blue}{-264} \\\Leftrightarrow & -2310x-539x& = & 70-264 \\\Leftrightarrow & \color{red}{-2849} x& = & -194 \\\Leftrightarrow & x = \frac{-194}{-2849} & & \\\Leftrightarrow & x = \frac{194}{2849} & & \\ & V = \left\{ \frac{194}{2849} \right\} & \\\end{align}\)