Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{4}{7})& = & 7x+\frac{8}{7} \\\Leftrightarrow & 24x+\frac{24}{7}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{168}{ \color{blue}{7} }x+ \frac{24}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 168x \color{red}{+24} & = & \color{red}{49x} +8 \\\Leftrightarrow & 168x \color{red}{+24} \color{blue}{-24} \color{blue}{-49x} & = & \color{red}{49x} +8 \color{blue}{-49x} \color{blue}{-24} \\\Leftrightarrow & 168x-49x& = & 8-24 \\\Leftrightarrow & \color{red}{119} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{119} & & \\ & V = \left\{ \frac{-16}{119} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{3}{11})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 18x+\frac{18}{11}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{396}{ \color{blue}{22} }x+ \frac{36}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 396x \color{red}{+36} & = & \color{red}{-110x} +33 \\\Leftrightarrow & 396x \color{red}{+36} \color{blue}{-36} \color{blue}{+110x} & = & \color{red}{-110x} +33 \color{blue}{+110x} \color{blue}{-36} \\\Leftrightarrow & 396x+110x& = & 33-36 \\\Leftrightarrow & \color{red}{506} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{506} & & \\ & V = \left\{ \frac{-3}{506} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{3}{5})& = & 5x+\frac{2}{9} \\\Leftrightarrow & -9x-\frac{9}{5}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-405}{ \color{blue}{45} }x- \frac{81}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -405x \color{red}{-81} & = & \color{red}{225x} +10 \\\Leftrightarrow & -405x \color{red}{-81} \color{blue}{+81} \color{blue}{-225x} & = & \color{red}{225x} +10 \color{blue}{-225x} \color{blue}{+81} \\\Leftrightarrow & -405x-225x& = & 10+81 \\\Leftrightarrow & \color{red}{-630} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-630} & & \\\Leftrightarrow & x = \frac{-13}{90} & & \\ & V = \left\{ \frac{-13}{90} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{5}{8})& = & -5x+\frac{8}{11} \\\Leftrightarrow & 6x-\frac{15}{8}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{528}{ \color{blue}{88} }x- \frac{165}{ \color{blue}{88} })& = & (\frac{-440}{ \color{blue}{88} }x+ \frac{64}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 528x \color{red}{-165} & = & \color{red}{-440x} +64 \\\Leftrightarrow & 528x \color{red}{-165} \color{blue}{+165} \color{blue}{+440x} & = & \color{red}{-440x} +64 \color{blue}{+440x} \color{blue}{+165} \\\Leftrightarrow & 528x+440x& = & 64+165 \\\Leftrightarrow & \color{red}{968} x& = & 229 \\\Leftrightarrow & x = \frac{229}{968} & & \\ & V = \left\{ \frac{229}{968} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{9})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -16x+\frac{8}{9}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1584}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1584x \color{red}{+88} & = & \color{red}{693x} +72 \\\Leftrightarrow & -1584x \color{red}{+88} \color{blue}{-88} \color{blue}{-693x} & = & \color{red}{693x} +72 \color{blue}{-693x} \color{blue}{-88} \\\Leftrightarrow & -1584x-693x& = & 72-88 \\\Leftrightarrow & \color{red}{-2277} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-2277} & & \\\Leftrightarrow & x = \frac{16}{2277} & & \\ & V = \left\{ \frac{16}{2277} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{5})& = & -3x+\frac{8}{9} \\\Leftrightarrow & 8x-\frac{4}{5}& = & -3x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{360}{ \color{blue}{45} }x- \frac{36}{ \color{blue}{45} })& = & (\frac{-135}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 360x \color{red}{-36} & = & \color{red}{-135x} +40 \\\Leftrightarrow & 360x \color{red}{-36} \color{blue}{+36} \color{blue}{+135x} & = & \color{red}{-135x} +40 \color{blue}{+135x} \color{blue}{+36} \\\Leftrightarrow & 360x+135x& = & 40+36 \\\Leftrightarrow & \color{red}{495} x& = & 76 \\\Leftrightarrow & x = \frac{76}{495} & & \\ & V = \left\{ \frac{76}{495} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{2}{11})& = & 7x+\frac{7}{3} \\\Leftrightarrow & 20x+\frac{8}{11}& = & 7x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{+24} & = & \color{red}{231x} +77 \\\Leftrightarrow & 660x \color{red}{+24} \color{blue}{-24} \color{blue}{-231x} & = & \color{red}{231x} +77 \color{blue}{-231x} \color{blue}{-24} \\\Leftrightarrow & 660x-231x& = & 77-24 \\\Leftrightarrow & \color{red}{429} x& = & 53 \\\Leftrightarrow & x = \frac{53}{429} & & \\ & V = \left\{ \frac{53}{429} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{4}{9})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 28x+\frac{28}{9}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1764}{ \color{blue}{63} }x+ \frac{196}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1764x \color{red}{+196} & = & \color{red}{-315x} +54 \\\Leftrightarrow & 1764x \color{red}{+196} \color{blue}{-196} \color{blue}{+315x} & = & \color{red}{-315x} +54 \color{blue}{+315x} \color{blue}{-196} \\\Leftrightarrow & 1764x+315x& = & 54-196 \\\Leftrightarrow & \color{red}{2079} x& = & -142 \\\Leftrightarrow & x = \frac{-142}{2079} & & \\ & V = \left\{ \frac{-142}{2079} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{3}{5})& = & -3x+\frac{8}{3} \\\Leftrightarrow & 8x-\frac{6}{5}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{-18} & = & \color{red}{-45x} +40 \\\Leftrightarrow & 120x \color{red}{-18} \color{blue}{+18} \color{blue}{+45x} & = & \color{red}{-45x} +40 \color{blue}{+45x} \color{blue}{+18} \\\Leftrightarrow & 120x+45x& = & 40+18 \\\Leftrightarrow & \color{red}{165} x& = & 58 \\\Leftrightarrow & x = \frac{58}{165} & & \\ & V = \left\{ \frac{58}{165} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{5}{4})& = & 5x+\frac{3}{7} \\\Leftrightarrow & -9x-\frac{15}{4}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-252}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{12}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -252x \color{red}{-105} & = & \color{red}{140x} +12 \\\Leftrightarrow & -252x \color{red}{-105} \color{blue}{+105} \color{blue}{-140x} & = & \color{red}{140x} +12 \color{blue}{-140x} \color{blue}{+105} \\\Leftrightarrow & -252x-140x& = & 12+105 \\\Leftrightarrow & \color{red}{-392} x& = & 117 \\\Leftrightarrow & x = \frac{117}{-392} & & \\\Leftrightarrow & x = \frac{-117}{392} & & \\ & V = \left\{ \frac{-117}{392} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{3}{10})& = & 5x+\frac{7}{3} \\\Leftrightarrow & -12x-\frac{9}{10}& = & 5x+\frac{7}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-360}{ \color{blue}{30} }x- \frac{27}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{70}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -360x \color{red}{-27} & = & \color{red}{150x} +70 \\\Leftrightarrow & -360x \color{red}{-27} \color{blue}{+27} \color{blue}{-150x} & = & \color{red}{150x} +70 \color{blue}{-150x} \color{blue}{+27} \\\Leftrightarrow & -360x-150x& = & 70+27 \\\Leftrightarrow & \color{red}{-510} x& = & 97 \\\Leftrightarrow & x = \frac{97}{-510} & & \\\Leftrightarrow & x = \frac{-97}{510} & & \\ & V = \left\{ \frac{-97}{510} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{3}{8})& = & -7x+\frac{3}{4} \\\Leftrightarrow & -10x-\frac{15}{8}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-80}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{6}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -80x \color{red}{-15} & = & \color{red}{-56x} +6 \\\Leftrightarrow & -80x \color{red}{-15} \color{blue}{+15} \color{blue}{+56x} & = & \color{red}{-56x} +6 \color{blue}{+56x} \color{blue}{+15} \\\Leftrightarrow & -80x+56x& = & 6+15 \\\Leftrightarrow & \color{red}{-24} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-24} & & \\\Leftrightarrow & x = \frac{-7}{8} & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)